/lit/ - Literature

[Anonymous No.10711040]

>starts with the greeks

>thinks he can move on from the greeks before he has even solved zeno's paradoxes

[Anonymous No.10711082]

>>10711040
something something calculus

[Anonymous No.10711088]

If we take in our hand any volume; of divinity or school metaphysics, for instance; let us ask, Does it contain any abstract reasoning concerning quantity or number? No. Does it contain any experimental reasoning concerning matter of fact and existence? No. Commit it then to the flames: for it can contain nothing but sophistry and illusion.

[Anonymous No.10711090]

>>10711040

What are limits?

[Anonymous No.10711102]

>>10711040
*unsheathes limits*
*derives behind you*
Heh, nothing personal, kid.

[Anonymous No.10711108]

>>10711090
That which is to overcome.

[Anonymous No.10711129]

Zeno was the ancient greeks version of a brainlet

[Anonymous No.10711145]

>>10711082
>>10711090
>>10711102
wrong

The basic problem is with divisibility, if you divide "something" infinitely you have infinite pieces of nothing, but in theory infinite pieces of nothing is "nothing". Etc. Very relevant at the time when they were fixated on categorizing and combining. "The one" vs the pieces of "The one"

From a quantum mechanics perspective it is actually very interesting as we discuss the quantized units related to atomic elements, photons, energy, waves, etc. Especially time is very interesting.

>>10711088
>Commit it to the flames
Someone is afraid, a man of knowledge need not destroy what he doesn't understand. Just avoid it.
Let the old intelligent condemn the bad and praise the good
Let the young intelligent pick up their torch.

Nigger

[Anonymous No.10711146]

1.999... = 2

[Anonymous No.10711148]

Is this the power of liberal education?

[Anonymous No.10711149]

>>10711146
By definition wrong

[Anonymous No.10711151]

>>10711146
...=0.001

[Anonymous No.10711158]

>>10711040
>in x amount of time Achilles runs 100 meter and the tortoise 10
>after x*2 amount of time after Achilles's start he has traveled 200 meter and the tortoise 120
I don’t get it

[Anonymous No.10711168]

>>10711158
you don't get it, the whole point is to show that paradoxes are a flaw in logic rather than a flaw in reality. the simple fact that the guy would clearly pass up the tortoise is evidence enough that the paradox is limited to such an extent that it shouldn't even be taken seriously besides the example it sets.

[Anonymous No.10711169]

>>10711149
>x=1
>By definition wrong
wat

[Anonymous No.10711180]

>>10711169
Numbers are artificial constructs with rules.
Two different numbers cannot be the equal to eachother.
By definition.

>>10711168
this can't be a serious comment

[Anonymous No.10711186]

>>10711180
why?

[Anonymous No.10711188]

>>10711180
1.999... and 2 aren't two different numbers. They are the same number.

[Anonymous No.10711194]

>>10711188
>1.999... and 2 aren't two different numbers. They are the same number.

[Anonymous No.10711195]

>>10711188
>postmodernism

[Anonymous No.10711197]

>>10711188
1.999... is infinitely lesser

[Anonymous No.10711199]

>>10711194
>>1.0 and 1 aren't two different numbers. They are the same number.
>>1/2 and 0.5 aren't two different numbers. They are the same number.
>>0 and -0 aren't two different numbers. They are the same number.

[Anonymous No.10711209]

>>10711186
>hur dur hes just talking about paradoxes, nothing to take seriously

There are a million ways to make paradoxes, why do you think every one of Zeno decided to study was based on the concept of division?

>>10711188
>>10711199
are you even trying?
try again without using the placeholder value 0

[Anonymous No.10711211]

>>10711199
They are practically "the same" but they simply aren’t

[Anonymous No.10711212]

anyone read this? is it good?

[Anonymous No.10711215]

>>10711212

[Anonymous No.10711216]

>>10711194
>>10711195
>>10711197
>>10711209
>>10711211
Sorry friendos but it's true. The last panel of >>10711188 contains a proof that 0.999... = 1
Therefore 1.999... = 1 + 0.999... = 1 + 1 = 2

[Anonymous No.10711217]

>>10711212
>THE ARGUMENTS OF ZENO OF ELEA
>THE PRECEDING CONSIDERATIONS implicitly contain the solution to all problems of the sort raised by Zeno of Elea in his famous arguments against the possibility of motion, or at least in what appear to be such when one takes the arguments only as they are usually presented; in fact, one might well doubt whether this was really their true significance. Indeed, it is rather unlikely that Zeno really intended to deny motion; what is more probable is that he merely wished to prove the incompatibility of the latter with the supposition, accepted notably by the atomists, of a real, irreducible multiplicity existing in the nature of things. It was therefore origi- nally against this very multiplicity so conceived that these argu- ments origiz~ally must have been directed; we do not say against all multiplicity, tc:lf it goes without saying that multiplicity also exists within its order>~s does motion, which, moreover, like every kind of change, necessarily supposes multiplicity. But just as motion, by reason of its character of transitory and momentary modification, is not self-sufficient and would be purely illusory were it not linked to a higher principle transcendent with respect to it, such as the 'unmoved mover' of Aristotle, so multiplicity would truly be non- existent were it to be reduced to itself alone, and did it not proceed from unity, as is reflected mathematically in the formation of the sequence of numbers, as we have seen. What is more, the supposi- tion of an irreducible multiplicity inevitably excludes all real con- nections between the elements of things, and consequently all continuity as well, for the latter is only a particular case or special

[Anonymous No.10711219]

>>10711215
but that's an even rating

[Anonymous No.10711221]

>>10711209
i just meant that it was a tool to show a flaw in a certain type of logic. not so much as something to not concern yourself with. i don't think i disagree with you, i don't comprehend the mathematical concepts Zeno was trying to display here, but I do know the guy must have known that in reality the tortoise would be caught up with eventually.

[Anonymous No.10711223]

>>10711216
>mathematical proof
Nice meme, kiddo

[Anonymous No.10711227]

>>10711217
>form of such connections. As we have already said above, atomism necessarily implies the discontinuity of all things; ultimately, motion really is incompatible with this discontinuity, and we shall see that this is indeed what the arguments of Zeno show.
>Take, for example·, the following argument: an object in motion can never pass from one position to another, since between the two there is always an infinity of other positions, however close, that must be successively traversed in the course of the motion, and, however much time is employed to traverse them, this infinity can never be exhausted. Assuredly, this is not a question of an infinity, as is usually said, for such would have no real meaning; but it is no less the case that in every interval one may take into account an indefinite number of positions for the moving object, and these cannot be exhausted in analytic fashion, which would involve each position being occupied one by one, as the terms of a discontinuous sequence are taken one by one. But it is this very conception of motion that is in error, for it amounts in short to regarding the con- tinuous as if it were composed of points, or of final, indivisible ele- ments, like the notion according to which bodies are composed of atoms; and this would amount to saying that in reality there is no continuity, for whether it is a question of points or atoms, these final elements can only be discontinuous; furthermore, it is true that without continuity there would be no possible motion, and this is all that the argument actually proves. The same goes for the argu- ment of the arrow that flies and is nonetheless immobile, since at each instant one sees only a single position, which amounts to sup- posing that each position can in itself be regarded as fixed and determined, and that the successive positions thus form a sort of discontinuous series. It is further necessary to observe that it is not in fact true that a moving object is ever viewed as if it occupied a fixed position, and that quite to the contrary, when the motion is fast enough, one will no longer see the moving object distinctly, but only the path of its continuous displacement; thus for example, if a flaming ember is whirled about rapidly, one will no longer see the form of the ember, but only a circle of fire; moreover, whether one explains this by the persistence of retinal impressions, as physiolo- gists do, or in any other way, it matters little, for it is no less obvious

[Anonymous No.10711231]

>>10711151
same applicability

[Anonymous No.10711235]

Hold on guys...

WTF even are decimals? Like what does "1.5" even mean? How could something be not 1 or 2 but something "in the middle"? What the hell does that mean?

[Anonymous No.10711237]

>>10711227
>that in such cases one grasps the continuity of motion directly, as it were, and in a perceptible manner. What is more, when one uses the expression 'at each instant' in formulating such arguments, one is implying that time is formed from a sequence of indivisible instants, to each of which there corresponds a determined position of the object; but in reality, temporal continuity is no more com- posed of instants than spatial continuity is of points, and as we have already pointed out, the possibility of motion presupposes the union, or rather the combination, of both temporal and spatial continuity.

[Anonymous No.10711243]

>>10711235
are you home-schooled or american?

[Anonymous No.10711244]

>>10711223
But then what kind of proof do you want?

[Anonymous No.10711245]

>>10711227
so basically it's I <3 Huckabees: the book

[Anonymous No.10711247]

>>10711223
>mathematical objects
>expect a non-mathematical proof
really makes you think

[Anonymous No.10711248]

>>10711216
>he thinks he can use nonsensical concepts like infinity in a proof
the only thing you proved was that you are a complete pseud

>>10711221
Your comment sounded dismissive, I must defend Zeno from the brainlets on this board that talk shit because they took a semester of pre-calc in highschool and think they know jack shit.

>>10711231
>tfw when you is a fish and you is swimming through the water but you doesn't even know the water there that you swimming through

[Anonymous No.10711253]

>>10711245
sorry, i don't watch movies

[Anonymous No.10711256]

>>10711231
>math is just faulty logic
Who in the everloving world would have thought?

[Anonymous No.10711260]

>>10711244
>>10711245
Math isn't real, you're using self-defined system to justify itself

[Anonymous No.10711263]

>>10711248
I understand, I probably didn't express myself as well as I liked. I was obsessed with paradoxes for a while as a kid. It felt like wordplay paradoxes were little perpetual motion machines of logic that wouldn't stop until you squared the circle by force of a gun. Do you think you could summarize what Zeno was trying to express by devoting his paradoxes to division?

[Anonymous No.10711266]

>>10711260
>you're using self-defined system to justify itself
yeah, that's basically what math is, your point?

[Anonymous No.10711268]

>>10711253
it's actually pretty much contingent on all of that.

https://www.youtube.com/watch?v=fjqjWC3Ycr4
this is all you need to see, really.

[Anonymous No.10711269]

>>10711235
>Like what does "1.5" even mean?
1 + 5/10.

>How could something be not 1 or 2 but something "in the middle"?
The real question here is how we can have something like 1/10 or 1/2. And the answer is, we just decide that every integer has a multiplicative inverse, that is a number you can multiply it by to get 1. The inverse of 1 is 1, the inverse of -1 is -1, and the rest we pretty much just pull out of our ass by writing 1/x for whatever x. It's pretty sneaky. And from there it's trivial to prove that 1 < 1.5 < 2.

>>10711248
>thinking the concept of a limit as n approaches infinity actually involves the concept of inifinity
It appears it is you who is the pseud.

[Anonymous No.10711274]

>>10711243
I think he means in the real world.
There's never 1.5 something.

[Anonymous No.10711276]

>>10711266
It’s circular reasoning and should not be taken seriously

[Anonymous No.10711278]

>>10711274
never seen half an apple?

[Anonymous No.10711279]

>>10711274
There's never even 2 something.

[Anonymous No.10711280]

>>10711278
You mean 2 uneven parts of a fruit?

[Anonymous No.10711282]

>>10711276
and why should we care about seriousness?

[Anonymous No.10711284]

this thread would've been deleted a year ago

[Anonymous No.10711285]

>>10711276
It's not circular reasoning, it's reasoning from axioms.

[Anonymous No.10711286]

>>10711280
if you insist in talking like a retard, i guess

[Anonymous No.10711287]

>>10711040
The mistake is that the interval of time between the steps of that diagramm (and thus his argument) are decreasing. Essentially, you are 'zooming in' to the moment where he will overtake the tortoise. Also this >>10711082

[Anonymous No.10711288]

>>10711282
>and why should we care about seriousness?
So I can this
Not an argument

[Anonymous No.10711293]

>>10711278
there's no longer an apple

[Anonymous No.10711294]

>>10711040
*scribbles some greek letters and other symbols on a blackboard*
*solves millenia-old problems*
*doesn't even have a degree*
Hehe.... kid...

[Anonymous No.10711296]

>>10711280
>2 parts
>1 fruit

So what you're saying is the apple as a concept is indivisible, and the parts are not the apple, but something else.

Thus, we can't say 0.5 of an apple, since there is no such thing.

[Anonymous No.10711297]

>>10711145
>but in theory infinite pieces of nothing is "nothing"
google what infinitesimals are. they are the very basis of integral calculation and thus many concrete subjects like electric fields.

[Anonymous No.10711299]

>>10711296
By Zeus, Socrates, you're right!

[Anonymous No.10711301]

>>10711296
>>10711293
this

[Anonymous No.10711302]

>>10711296
Correct, these 2 parts are entirely unique

[Anonymous No.10711303]

>>10711280
what's a part?

[Anonymous No.10711305]

>>10711040
The series 1+1∕2+1/4+1/8+...1/2^n is convergent and S = 2. Solved.

[Anonymous No.10711309]

>>10711303
The determiner of "sameness" in that sentence

[Anonymous No.10711310]

>>10711284
lol faggot

[Anonymous No.10711315]

>>10711302
What is their most prominent feature? Being like an apple, but (you can substite into here a calculation of the number of seeds, the amount of pulp and skin, the mass etc.)
Thus it seems reasonable to posit they're like an apple, but not like a full apple. If only we could represent that mathematically or with language...

[Anonymous No.10711327]

>>10711263
I definitely find Zeno's paradoxes have much more content than the common logic/word paradox ("This a lie".... etc ). I study physical chemistry and dividing matter and energy into pieces is something we only developed in the past 100 years.

We genuinely cannot fathom how divisible matter is, animals are made of molecules, made of elements/atoms, made of proton/neutrons/electrons, made of quarks and shit, made of xx, made of xx .... made of waves? spooky nigga

Now with zeno's paradox contain the concept of time, can we possible quantize time? What even is time? There would be no time if there was no energy, if there was no motion we couldn't perceive of time. The more times we divide time the slower it gets, if we had infinite brain loading speed, time wouldn't progress.
The Godmind

>>10711297
ur like a little baby to me, go play with you reimann sums

>>10711269
you literally have autism, I can tell
typical purist mathfag

>>10711296
>>10711301
>>10711280
>>10711278
QUANTIZE

>>10711284
idk about a year ago, >>10711217 this guy recommended a book I will look into so its not a complete waste. Sorry Zeno doesn't have much primary literature.

[Anonymous No.10711329]

>>10711315
We could but the result would be too vague, so we should just stick to living in caves and hitting rocks with sticks

[Anonymous No.10711330]

>>10711082
the ancient world didn't have a concept of infinity. They also had no concept of 0.

[Anonymous No.10711333]

>>10711330
lol

[Anonymous No.10711336]

>>10711315
If a bystander came upon half an apple, what would lead him to consider that it was, in fact, a half, and not already whole in itself? But one who had seen a full apple would consider him foolish, and perhaps rightly so, but do we know that an apple is in itself full, and not in fact, merely one half of something else? For, despite this consideration, we are inclined to believe that there is some meaning in the notion of "an apple", a unity, a wholeness of completeness, which is not a negative or a positive of something but in fact completed, perhaps even annihilated, and it is this annihilation of opposites which actually constitues the full apple, which is at rest and thereby able to "be" a thing in itself. But can we know that the apple does not in fact constitute one half of something else? If two halves of an apple arise out of one apple, and the first man mistook this for a whole, whence arose the apple if not by division of something else? If we are unable to provide an explanation, then the person in our example who criticized the other for thinking that a half of something was in fact a whole something is guilty of the same criticism, in thinking that the apple is whole in itself.

[Anonymous No.10711338]

>>10711327
>you literally have autism, I can tell
>typical purist mathfag
rude

[Anonymous No.10711339]

>>10711330
>the ancient world didn't have a concept of infinity

[Anonymous No.10711342]

>>10711336
>an apple is a 30th of a tree

[Anonymous No.10711343]

>>10711327
yeah i don't think we disagree at all. i've been pretty similarly inclined for quite some time. it's stonerthought regarding time for sure. seriously though, this is i <3 huckabees. just watch the first 2 minutes of this vid and tell me it isn't all the same conversation over and over again, yin and yang, wave and particle, blah and yaddah. you know what it do.
https://www.youtube.com/watch?v=fjqjWC3Ycr4

[Anonymous No.10711345]

>>10711336
The man who has seen an apple tree would call the man who has only seen an apple foolish

[Anonymous No.10711357]

>>10711345
>But this new world is perfectly realised just as little as the new-born child; and it is essential to bear this in mind. It comes on the stage to begin with in its immediacy, in its bare generality. A building is not finished when its foundation is laid; and just as little, is the attainment of a general notion of a whole the whole itself. When we want to see an oak with all its vigour of trunk, its spreading branches, and mass of foliage, we are not satisfied to be shown an acorn instead. In the same way science, the crowning glory of a spiritual world, is not found complete in its initial stages. The beginning of the new spirit is the outcome of a widespread revolution in manifold forms of spiritual culture; it is the reward which comes after a chequered and devious course of development, and after much struggle and effort. It is a whole which, after running its course and laying bare all its content, returns again to itself; it is the resultant abstract notion of the whole. But the actual realisation of this abstract whole is only found when those previous shapes and forms, which are now reduced to ideal moments of the whole, are developed anew again, but developed and shaped within this new medium, and with the meaning they have thereby acquired.

[Anonymous No.10711359]

>>10711339
>>10711345
What's but a leaf?
Where's the atmospheres' end?
Who can say where one thing ends and another begin?

[Anonymous No.10711362]

>>10711345
This is where I am not sure, for it seems very clear, intuitive that a half of an apple is in fact a half of an apple, and not something in itself, whereas the "rest of the tree" does not seem a half of the tree, but as >>10711342 says, if we are even to consider the apple as a fraction of the tree, we must consider it not half but much less, but this is only in regards to size, or mass, or density, and each of these would likely constitute a different fraction of the whole tree.

Now then, are we to say that a thing, such as an apple, can be one fraction of one thing and one fraction of another thing? As in, it is 1/30th of a tree, but also 1/60th of two trees? It seems to me that here we are not speaking of the apple anymore but merely the size of one object in relation to the size of another object, whereas in the example of the "half of an apple", we are not merely considering it in terms of the "size of this piece of matter" in relation to the "size of this twice as large piece of matter", but as something else, as a half of one essence, and the essence, considered in the metaphysical sense being the important part.

[Anonymous No.10711373]

>>10711343
Well everything we percieve is nonsensical if you have no concrete perspective to view it from.

That is why humans are so indebted to the only axiom.

Everyone then who hears these words of mine and does them will be like a wise man who built his house on the rock. And the rain fell, and the floods came, and the winds blew and beat on that house, but it did not fall, because it had been founded on the rock.

[Anonymous No.10711374]

>>10711194
>brainlet posters are THIS mathematically illiterate

[Anonymous No.10711377]

>>10711373
i do believe that philosophically we are of the same spirit. though i do find that the rocks are in too short supply for my reckoning.

[Anonymous No.10711378]

>>10711362
When we consider the notion of a half of an apple, we are not merely discussing size, since a third of an apple would have something in common with a half of an apple, in that both are considered as parts of an apple, and not merely as objects. There is something "apple-ish" about them, but where does the apple-ishness end? This is where it seems to delve into absurdity, since it seems that at a certain point, a sliver of an apple would become so small as to constitute seemingly nothing at all. It seems pertinent to consider the different parts of the apple considered as things in themselves, such as the flesh, the seed, the skin, the top and the bottom, and so forth. For, the top half of an apple would not match the bottom half, nor, even, would two halves of a vertical slice match each other, since I have never seen a perfectly symmetrical apple, and cannot prove that such a one exist, although neither can I determine that one does not exist either.

So when we are talking of one half of an apple, we cannot be said to, as far as we know empirically, be considering anything which has any basis in reality, since there is no "half of an apple" that is in fact perfectly one half, since every apple has its own unique asymmetry which does not lend itself to such precise divisions. Is it even possible to actually "slice and apple in half"? Or when we say this do we merely mean it approximately?

[Anonymous No.10711379]

>>10711362
The half of an apple comes from an apple, just like the apple comes from an apple tree, just like the apple tree comes from the proto-apple tree, just like the proto-apple tree comes from the proto-proto-apple tree, etc
We're applying ideas like wholeness and sameness to things we cannot fully grasp

[Anonymous No.10711382]

>>10711379
But it seems that half of an apple is, in fact, a half of an apple, whereas an apple is not half of an apple tree.

[Anonymous No.10711385]

>>10711382
You're doing it again, you’re applying concepts of sameness and wholeness to things you cannot fully understand

[Anonymous No.10711403]

>>10711373
t. JP

[Anonymous No.10711414]

>>10711373
>not coupling multiple conflicting axioms to contradict inferior logic systems
perspective is more contingent on the status of the wise man himself, not the rock. if one relies more on that vision rather than the structure of his flesh and the interpretation of the data, then they will lead themselves over a number of cliffs.

[Anonymous No.10711417]

>>10711385
Then are all things merely appearances? Is it merely an appearance for me to eat a fruit which is poisonous instead of a fruit that is not poisonous? Is my resulting death merely an appearance, and there was in fact, no apple to begin with, no fruit, no me, no poison, no digestion, no life, and no death?

[Anonymous No.10711437]

>>10711403
Thanks I have been looking for that picture.

Peterson is brainlet, his statement is out of necessity, he had his ideas and looked for a way to justify them. The man doesn't believe and is constantly chased by his demons because of it.
The idea that humans can know all is utter hubris. The jump from human knowledge to divine knowledge can only be achieved through faith in the unknowable.

>>10711414
There is and can only be one truth.

[Anonymous No.10711466]

>>10711194
Man I love the retarded wojak meme

[Anonymous No.10711468]

>>10711466
>I love the retarded wojak meme

[Anonymous No.10711486]

>>10711378
by that standard we can't either talk about an apple, as the apple is slowly rotting and accreting or losing mass all the time

[Anonymous No.10711500]

>>10711486
You're right. As for where to go from here I've given up as it is clear man cannot attain to the divine by his own strength but only by faith in God alone.

[Anonymous No.10711502]

>>10711040
BTW you can't use limits because limits are an incoherent concept

[Anonymous No.10711512]

>>10711417
Nope, just saying everything is unique and nothing's the same.

[Anonymous No.10711520]

>>10711502
>limits are an incoherent concept

[Anonymous No.10711530]

>>10711040
pure sophistry

[Anonymous No.10711532]

>>10711520
I'll prove it once I get home.

[Anonymous No.10711568]

>>10711532
>phoneposter
not surprised

[Anonymous No.10711610]

>>10711082
>>10711102
LOL, analysis does not solve Zeno's paradoxes: you assume that the mathematical model of the continuum (R) is the reality... Not to mention all the logical troubles with the definition of R.

[Anonymous No.10711612]

>>10711287
You are really far off from understanding what Zeno's actual argument is.

[Anonymous No.10711627]

>>10711520
https://www.youtube.com/watch?v=kcirwIwRIUw

[Anonymous No.10711628]

>>10711082
>>10711287
>CALCULUS!

Idiots who understand neither maths nor philosophy.
When you have potentially infinite increments towards a single limit how is it possible IN EXPERIENCE to transition past those infinite increments?

[Anonymous No.10711688]

>>10711188
>>10711194
they are the same number, brainlet. read about construction of the real numbers:

https://en.wikipedia.org/wiki/Construction_of_the_real_numbers#Construction_from_Cauchy_sequences

the cauchy sequence version is easiest to understand.

[Anonymous No.10711693]

>>10711688
>they are the same number, brainlet

Nigger every number is the same number by that logic which erases the point of numbers

[Anonymous No.10711698]

>>10711693
you didn't understand it. put down the zeno and pick up rudin.

[Anonymous No.10711707]

>>10711698
Not an argument
If 1.9999... is the same as 2 then 1.98999... is the same as 1.9999... and so on until you reach zero and infinity

[Anonymous No.10711709]

Does anyone else think this paradox is similar to the problem of being in time? I mean that the future is never here, and the present is constantly becoming the past, so "when" is the "present" and how does it change?

If I recall Augustine tried to address this difficulty in Confessions but I don't remember him getting anywhere.

How can that which IS (the present), change into that which IS NOT (the future). How can that which is change at all? How can something which is not yet, yet be something that is to be?

It seems as though that which we think is not is merely something which we are not able to perceive due to the limitations set upon our faculties of knowing. So the changes we are perceiving are actually all things which are, only that we can only perceive the all in a sort of chronological, sensible way. He who knows all that is must no longer be constrained by time, seeing as how such a being could never experience one moment as not yet having occurred. Therefore it is our own limitations which lead to the problems set before us in logic. They are not problems in reality. It is our own limitation which we see when we consider that the future seems not to have happened yet, when in reality it has happened, only our limited vehicle for experiencing them can only perceive it as something unattainable except in a rudimentary way.

[Anonymous No.10711712]

>>10711707
>If 1.9999... is the same as 2 then 1.98999... is the same as 1.9999...

does not follow, in any way.

[Anonymous No.10711714]

>>10711709
Best post in the thread

[Anonymous No.10711717]

>>10711712
>does not follow, in any way.

Why not, abstractly they're the exact same increment

[Anonymous No.10711722]

>>10711717
no they aren't.

1.9899999... converges to 1.99 exactly.

[Anonymous No.10711728]

>>10711722
Right whatever so lets say 1.999...8

[Anonymous No.10711729]

>>10711707
>If 1.9999... is the same as 2 then 1.98999... is the same as 1.9999... and so on until you reach zero and infinity
by that logic 1.98999... is the same as 1.99 though you fucking retard

[Anonymous No.10711731]

>>10711729
See >>10711728 you pedantic jackass

[Anonymous No.10711732]

>>10711728
>1.999...8

there is no such thing.

[Anonymous No.10711733]

>>10711728
>1.999...8
You can't do that. What place value does that last 8 have?

[Anonymous No.10711734]

>>10711728
an infinite series doesn't end so that's not a number

[Anonymous No.10711735]

>>10711732
Neither is there such thing as 1.9999...

[Anonymous No.10711739]

>>10711733
Its potentially infinite, but were you to arrive at it, it would be 8, just like with 1.999 is infinite but were you to arrive at the end it would be 9

[Anonymous No.10711740]

>>10711731
>pedantic

no, you're being sloppy, resulting in trivial errors of reasoning.

>>10711735
there is. it's a cauchy sequence.

[Anonymous No.10711742]

>>10711735
Yes there is. It's also known as 2.

[Anonymous No.10711745]

Don't Planck units solve Zeno's Paradox?

[Anonymous No.10711749]

>>10711740
Trivial being the emphasis you hautey faggot

[Anonymous No.10711753]

>>10711742
Thats ok, so is 1.999...8 syllogistically

[Anonymous No.10711756]

>>10711745
No, even if they were real it still leaves the question of how one transitions from one plank to another

[Anonymous No.10711758]

>>10711745
no, there's a common misconception that planck units are like the "pixels of the universe" or whatever, but they're nothing like that. they're just the scales beyond which the standard model doesn't make meaningful predictions.

>>10711753
no, that's completely nonsensical. it doesn't "end" with anything.

[Anonymous No.10711760]

>>10711739
That ain't how it works my dude, you have to be able to say what value each digit has. That's possible for every 9 in 1.999...

>>10711753
There's no such number as 1.999...8.

[Anonymous No.10711764]

>>10711739
>potentially infinite
>but if you were to arrive at it
>it would be 8

can you rigorously and consistently define all three of these things?

[Anonymous No.10711769]

>>10711760
>you have to be able to say what value each digit has

I can though, give me any number and I'll give you its value, in the case of every single one but infinite it will be 9

[Anonymous No.10711772]

>>10711769
>every single one but infinite
what do you mean by this? there is no such thing as an "infinitieth" digit.

[Anonymous No.10711771]

>>10711758
>no, that's completely nonsensical

So is the original proposition which is my point

[Anonymous No.10711780]

>>10711771
no, the fact that 1.999...8 is nonsensical does not imply that 1.9999... is nonsensical. I have already explained why, if you're still not satisfied all I can do is recommend you pick up a real analysis text.

[Anonymous No.10711783]

>>10711520
>first year mathlet thinks writing out a limits expression is proof enough

[Anonymous No.10711785]

>>10711628
You can't experience infinitesimaly small increments, that's a mathematical abstraction. Zeno's paradox is about mathematical objects and has no relation to reality.

[Anonymous No.10711794]

>>10711785
>You can't experience infinitesimaly small increments

So you're saying the divisibility of time is a product of consciousness

[Anonymous No.10711799]

>>10711771
if you reject 1.9999... that's ok but you have to reject all real numbers, like the square root of 2, so you have to reject that the diagonal across a square with sides of one unit of length exists

[Anonymous No.10711801]

>>10711780
You haven't explained shit. You've just been reverting to truisms and hiding behind an imagined authority. Learn your own theories before LARPing like you know it

[Anonymous No.10711805]

>>10711799
Well that's ok since 2 does not exist outside abstraction, much like rational numbers

[Anonymous No.10711808]

>>10711801
explain to me how 0.999...8 is a coherent concept.

[Anonymous No.10711816]

>>10711808
First explain to me how 0.999... is a coherent concept for that question to matter
As far as I see all we're dealing with are numbers that are assigned abstract descriptions. 0.999... is described as infinitely regressing with 9's and 0.999...8 also infinitely regresses with 9's but its infinite digit must always be derived as 8

[Anonymous No.10711825]

>>10711805
1 doesn't exist either

[Anonymous No.10711831]

>>10711816
there's no such thing as an infinite digit

[Anonymous No.10711837]

>>10711831
Why not?
If we take f(n) to derive any particular integer along the number then f(∞) must derive 8
If there's no such thing as the infinieth digit its only because there's no such thing as infinity making 1.999... just as illegitimate of an expression

[Anonymous No.10711841]

>>10711714
The question is, what is our meaning in the world as limited beings?

There seems to be three possibilities:

1) We can never surpass our limitations and must remain within a finite, mortal, incomplete state of existence. I.e., a meaningless mortality.
2) We cannot surpass our limitations, but there is some context to this wherein a higher objective is placed above the desire to know everything. I.e., a meaning to mortality.
3) We can surpass our limitations, and also trap ourselves within greater constraints, and divine knowledge is at least potentially attainable through other means.

I am inclined to believe that 2 is almost an absurdity, and that it is actually a choice between 1 and 3, since there being a meaning to our limited existence is itself a factor which broadens our horizons.

It at least seems to be the case that our capacities can be limited even further, either temporarily through intoxication by substance or by passion, or permanently by brain damage or other impairments. And even if we are to adopt the most positivist outlook of the world, it seems clear that the capacity for reason did not arise out of nothing but developed either accidentally or deliberately (but how a creature could deliberate its own development to a higher state of being from a lower state seems incomprehensible). Therefore if we concede that limitations themselves are not fixed but simply inherent properties of different organizations of things, we again either seem to posit that they are accidental and incomprehensible, or comprehensible and able to be surpassed. But if we are to say that man can overcome his own limitations an ascend into a higher domain which he was not born into, how are we to explain the position that he got to the point where he could become aware of limitations in the first place? Since he certainly would have had to surpass a considerable limitation in willing himself from a beast into a rational human being without yet being a rational entity.

Or are we to say that that which is required for the arising of life is something which is inherent to the properties of nature, in that they are imbued with a certain order which predisposes them to such an organization that rational creatures, over time will inevitably be produced under certain conditions, at which point, man is able to take over and complete the work which nature began? This certainly points to a supernatural imposition which occurred in the first place, and indeed seems necessary if we are to admit that anything limited could come into being in the first place.

[Anonymous No.10711853]

>>10711816
>First explain to me how 0.999... is a coherent concept for that question to matter

it is the sum of the series: 0.9 + 0.09 + 0.009 + 0.0009 ...

this is the limit of the sequence of partial sums: 0.9, 0.99, 0.999, 0.9999 ...

which is 1.

>but its infinite digit

now tell me how such a thing as an "infinit digit" is a coherent entity.

[Anonymous No.10711855]

>>10711837
If we take f(n) to derive any particular integer along the number then f(∞) must derive 8

∞ is not a number.

[Anonymous No.10711856]

>>10711837
you can have the reals + ∞ but things get weird then
https://en.wikipedia.org/wiki/Extended_real_number_line

[Anonymous No.10711858]

>>10711853
>now tell me how such a thing as an "infinit digit" is a coherent entity.

The same way you just declared an infinity series of summations as a coherent expression

[Anonymous No.10711864]

>>10711855
>∞ is not a number.

I agree, and neither is 1.999...

[Anonymous No.10711865]

>>10711858
it's a coherent expression because you can define it with limits, and limits can be put on a rigorous footing without reference to "completed infinities" via epsilon-delta constructions. the same cannot be said for "infinitieth digit".

[Anonymous No.10711867]

>>10711865
>it's a coherent expression because you can define it with limits

You can do the same with 1.999...8 limit it wherever you want and you can derive a concrete number

[Anonymous No.10711871]

>>10711855
∞ is a number in the extended reals. But anon's function isn't well defined with that domain.

[Anonymous No.10711875]

>>10711867
>You can do the same with 1.999...8

show me.

[Anonymous No.10711880]

>>10711745
No. Current models of spacetime are continuous, Planck volumes and such have no deep physical significance.
People often think everything is quantized in quantum mechanics... not true.

[Anonymous No.10711881]

>>10711875
Its the same process as earlier, limit the regression to seven integers and you recieve 1.999999 and so on, until you reach infinity whereupon you receive 8

[Anonymous No.10711891]

>>10711881
what's 1.999...8 + (1.999...8 / 2) = ?

[Anonymous No.10711892]

>>10711881
>until you reach infinity
but you won't. If it's the same process "until you reach infinity" then it's just the same process.

[Anonymous No.10711897]

>>10711892
And hence why its the same number as 1.999... as are all numbers

[Anonymous No.10711898]

>>10711881
what do you mean "limit the regression to seven integers"?

i don't think you have the faintest idea what a limit is.

[Anonymous No.10711907]

^everyone above is a brainlet

[Anonymous No.10711911]

>>10711897
>hence why its the same number as 1.999...
ok then

>as are all numbers
but no

[Anonymous No.10711918]

>>10711911
>but no

But of course, because then we're rendering equivalent 1.999...7, 2.000...1 and so on until you reach zero and infinity

Effective equivalence is not the same as actual equivalence.

[Anonymous No.10711928]

>>10711897

[Anonymous No.10711931]

>>10711918
But how will changing the last digit give you anything other than 2?

[Anonymous No.10711946]

i have to leave now, but if you want to do this from absolute first principles you need to do the following:

- construct the natural numbers from set theory. there is an actual "completed infinity" lurking here, the only one. whether its existence "contaminates" everything thereafter is a matter of philosophy or taste, but in a practical sense you won't be able to do much useful mathematics without it. finitism is a meme.
- construct the integers from the naturals
- construct the rationals from the integers
- construct reals from the rationals by cauchy sequences, or alternatively use another approach like the purely field-axiomatic one. this is the trickiest step and requires you to have a rigorous understanding of limits, convergence, etc.
- give 0.999... an unambiguous meaning in terms of this construction
- show that this meaning is equivalent in every way to the number 1

[Anonymous No.10711955]

>>10711931
Because there's no limit of the extension from 0.000...1 and 999...9.999...
They are all of course equivalent to 2

[Anonymous No.10711980]

>>10711955
Prove 1 = 2

[Anonymous No.10711994]

>>10711610
>logical troubles with the definition of R
Wildberger pls leave
the real numbers have been rigorously defined since the time of Dedekind

[Anonymous No.10711997]

I'm a mathematician and reading this thread gave me a brain hemorrhage.

>>10711946
>>10711853
Know what they're talking about. The rest of you are varying degrees of misinformed.

[Anonymous No.10712001]

>>10711980
If 1.999...=2
Shouldn't
>1 = 1.000...111...=eventually= 1.000...222... = 1.000...333... = 1.111... = 1.222... = 1.333... =1.333...4... = 1.999... = 2

[Anonymous No.10712007]

>>10712001
>1.000...111...
how many zeros come before the first 1?

[Anonymous No.10712008]

>>10711997
>My misconstrued language games aren't wrong y-you just don't get it

Absolute state of mathfags

[Anonymous No.10712009]

>>10712007
infinite

[Anonymous No.10712012]

>>10712001
>1.000...111...

does not exist

[Anonymous No.10712018]

>>10712008
the only one misconstruing things here is (You)

[Anonymous No.10712023]

>>10712009
that is not a well defined construction
you can't have an "inifith" digit
every digit is at a finite place, just because there are an infinite number of them in total doesn't change the fact that every digit is preceded by a finite amount of digits

[Anonymous No.10712026]

>>10712008
Give me a specific example of what you think is a "misconstrued language game"

[Anonymous No.10712036]

>>10712001
>>10712023
To clarify anon, you need to provide a formula a(n) for the digits of your number. I can do 1.99999 because I can define a(0) = 1, a(n > 1) = 9. You can't do that for 1.000...111...

[Anonymous No.10712038]

>>10712026
Declaring that a number of which the most can be said of it is that it is less than 2 is equal to 2. From there its just a matter of unraveling the nonsense from which you attempt to justify such a stupid assertion

[Anonymous No.10712042]

>>10712023
but
is 1.888... = 1.888...9
?
why does an infinity of .999... become 2
when an infinite of .888... does not become ...9
>Full glass of water
>Remove one water molecule
Is it no longer a full glass of water?

[Anonymous No.10712043]

>>10712036
you don't have to provide an explicit formula
in fact almost all numbers have no such formula (uncomputable numbers) but every digit still needs to have its well defined place
there is no such thing as the "infinith" digit so no digit can come after that one

>>10712038
>I failed high school math: the post
https://en.wikipedia.org/wiki/0.999......

[Anonymous No.10712045]

>>10712038
>of which the most can be said of it is that it is less than 2

but that isn't what's happening. pay closer attention. a sequence need not contain its limit.

[Anonymous No.10712050]

>>10712042
why would 0.888... do anything unusual?

[Anonymous No.10712052]

>>10712043
>Hah I'll link to a wikipedia article which explicitly says that the subject is an issue of debate among mathematicians I win

Right you're an unserious person

[Anonymous No.10712057]

>>10712038
In the context of the continuum (which is NOT a good model of physical reality, if you're going to protest that):

(1) absolute differences are non-negative, ie, it's 0 or it's positive
(2) two numbers are equal if their absolute difference is zero
(3) the difference between 1.999... and 2 can be shown to be smaller than ANY positive number
(4) therefor, by (1), the difference between 1.999... and 2 is zero
(5) so by (2) 1.999... = 2

which statement do you feel is nonsensical?

[Anonymous No.10712058]

>>10711235
This is the funniest shit I have ever read

[Anonymous No.10712060]

>>10712043
>Although the real numbers form an extremely useful number system, the decision to interpret the notation "0.999..." as naming a real number is ultimately a convention,

Impressive citation

[Anonymous No.10712064]

>>10712052
>explicitly says that the subject is an issue of debate among mathematicians

it doesn't say that.

[Anonymous No.10712065]

>>10711994
>Dedekind
sounds like a meme

[Anonymous No.10712067]

>>10712036
maybe
>1.∞1∞ = 1.∞2∞
is better?
(I'm arguing "against" 1.999=2; even though I'm also >>10711146)

>>10712050
>why would 0.999... do anything unusual?

[Anonymous No.10712068]

>>10712043
You don't have to provide a formula but it has to be expressible as a formula. We're saying the same thing.

[Anonymous No.10712072]

>>10712067
>1.∞1∞ = 1.∞2∞
Define what this means, preferable in the context of a summation

[Anonymous No.10712073]

>>10712042
>>Full glass of water
>>Remove one water molecule
integers are not reals

[Anonymous No.10712074]

>>10712060
ignoring the part that comes right fucking afterwards

>However, it is by no means an arbitrary convention, because not adopting it forces one either to invent strange new objects or to abandon some of the familiar rules of arithmetic.[48]

if 0.999... is to have any unambiguous, coherent meaning, we are forced to accept that it is equal to 1.

[Anonymous No.10712078]

>>10712042
1.88.... is a well defined number and is exactly equal to 17/9
1.88...9 is not, again every digit must have a well defined place, you can't tell me where that 9 is because that number doesn't make any sense

>why does an infinity of .999... become 2
it doesn't "become" anything
there are many ways to prove 0.99..=1, see the wikipedia link, but the easiest way to conceptualize it may be to consider the fact that 1-0.99..=0.00.. = 0 so they have to be the same

>>10712052
please point to the part -preferably with quotes- where it says that this is a topic of debate among actual mathematicians

>>10712060
that's actually fair but the point is that there is no reason not to allow the convention because there is no ambiguity since the number is well defined, consistent, logical and behaves well

>>10712067
no that's still terrible
you can't have any digit followed by an infinite number of digit, that simply does not make sense

>>10712068
unless you count just the set of the digits {1,3,6,3, random shit...} a "formula" then that formula need not exist

[Anonymous No.10712080]

>>10712074
Changing of rules does not imply incorrect. We are interested in reflecting reality here

[Anonymous No.10712083]

>>10712067
because the sequence 0.9, 0.99. 0.999 ... has a limit equal to 1.

the sequence 0.8, 0.88, 0.888 ... doesn't have any limit other than the real number 0.888...

[Anonymous No.10712088]

"0.999..." is not a number

[Anonymous No.10712089]

>>10712080
content-free reply

[Anonymous No.10712090]

>>10712078
>because there is no ambiguity since the number is well defined, consistent, logical and behaves well

Yet is patently fucking ridiculous

[Anonymous No.10712095]

>>10712089
Next time I'll just say not an argument

[Anonymous No.10712097]

>>10711994
>>10712065

[Anonymous No.10712099]

>>10712090
no doubt it's unintuitive at first but when you get used to working with limits and infinite series and start understanding the cauchy sequence convergence definition of the real numbers then not allowing the number starts looking like the bizarre part
it all flows so naturally and fluidly once you get further into math even though it's little more than a fun logical puzzle if you've never gone beyond high school math

[Anonymous No.10712100]

>>10712090
how is that any different from just saying "i don't like it"?

all it really boils down to is the fact that some real numbers have more than one decimal representation.

[Anonymous No.10712102]

>>10711231
Wait, I just realized. How is it possible to divide a glass of water into thirds? If 1/3 is 0.3333..., how could you divide a finite number of molecules into thirds? The end result would not be three glass of water, each with 1/3 of the water, but finite, unequal parts.

And moreover, if the glass of water had an odd number of molecules, you could not even divide it into two glasses equally, unless you were to divide the molecules in half, and this would merely be to reduce the number of parts to an even number, which could then be split in half.

So how is it that 1/2 sometimes constitutes a real possibility, and sometimes not?

[Anonymous No.10712105]

>>10712102
if the number of molecules is divisible by three then there is no problem.

[Anonymous No.10712115]

>>10711339
Zeno was the first to describe it but as we can see in his paradoxes he failed to grasp it in a mathematical sense. Thousand years later it drove cantor insane

[Anonymous No.10712116]

>>10712100
Because all this rests on the notion that infinitely small numbers don't "exist" yet uses these very same infinitely small numbers to express this "alternative" representation

[Anonymous No.10712117]

>>10711610
Fuck off, Wildfag

[Anonymous No.10712125]

>>10712116
there are no infinitesimals in the canonical constructions of the reals.

[Anonymous No.10712130]

>>10712125
>canonical

[Anonymous No.10712133]

>>10712130
?

you can construct the reals using surreal or hyperreal numbers if you want, but it's not necessary by any means.

[Anonymous No.10712134]

>>10712105
But if it isn't divisible by three, then there are certain glasses of water out there that can be split into thirds, and other glasses of water which can't, which is to say that a glass of water can sometimes be split into three, and sometimes not.

Thinking of that glass of water which cannot be split into thirds (perhaps the very one sitting on my desk as we speak!), what meaning, then, does 0.3333.... actually have? It is to say that 1/3 is not a possibility, or that it is only possible to speak of 1/3 concretely as a conditional value. But this is to say that "1/3" is not a real thing.

My concern is this: what does it mean if I cannot split a glass of water into thirds?

[Anonymous No.10712140]

>>10712117

[Anonymous No.10712154]

>>10712134
>My concern is this: what does it mean if I cannot split a glass of water into thirds?

it means you can't split a glass of water into thirds. i.e. the water example isn't a completely valid model of how the real numbers work.

but on the other hand if you're going to take it completely physically literally it's irrelevant anyway because there will always be an exchange of >trillions of particles with the environment due to evaporation and condensation. why worry about it?

[Anonymous No.10712170]

>>10711728
That's a terminating decimal you fucking brainlet

[Anonymous No.10712179]

>>10712170
Yes, and?

[Anonymous No.10712181]

>>10711040
Zeno's paradox becomes invalid by becoming aware of the planck length and the realization that space is not at all infinitely divisible.

[Anonymous No.10712184]

>>10712179
Then what kind of point are you trying to prove? We're talking about decimals that don't terminate, idiot

[Anonymous No.10712187]

>>10712181
Proofs?

[Anonymous No.10712193]

>0.899... = 0.9

[Anonymous No.10712204]

>>10711997
I feel that anon; I'm a math major. But, what did we expect from a literature board?

[Anonymous No.10712205]

>>10712181
that's not what the plank length means

but even assuming that's the case that just raises more questions than it answers
time and space seem to be two sides of the same coin so that would imply time isn't infinitely divisible either
so how does speed work? how does traveling more planck lengths in fewer planck time units work? how does the expansion and stretching of spacetime work? how does this square with relativity in general?

[Anonymous No.10712207]

>>10712193
Yes it does under the conventional interpretation of "=" and "99..."

[Anonymous No.10712217]

>>10712184
No I'm pretty sure we're talking about natural numbers

[Anonymous No.10712227]

>>10712217
Only positive integers and fractions of positive integers are natural, the rest don't actually exist

[Anonymous No.10712229]

>>10712205
If an object moves at increasingly smaller distances then quantum mechanics invariably comes into play, which breaks down at planck length level. Same with time. Eventually the fastest they can possibly go is one planck length per planck time.

[Anonymous No.10712231]

>>10712217
But 0.999...8 isn't a natural number you fucking lampoon
>>10711997
Same here

t. math major
>>10712008
>hurr durr I read Wittgenstein i am so smaret

[Anonymous No.10712235]

>>10712231
>But 0.999...8 isn't a natural number you fucking lampoon

Obviously, but my point is it was disingenous to imply we were talking ABOUT non-terminating decimals when 2 clearly isn't

[Anonymous No.10712236]

Anyone know any books on aesthetics?
Not art but philosophy of beauty.

[Anonymous No.10712240]

>>10712229
>which breaks down at planck length level. Same with time
this is both conjecture right?
hasn't like every empirical experiment on loop quantum gravity come out negative?

[Anonymous No.10712246]

>>10712236
Fuck off homo

[Anonymous No.10712247]

>>10711194
>>10711195
>>10711197
>>10711209
>>10711211
...etc.

You guys should read a bit about what we mean by using real numbers. It's actually a very interesting problem to make a good definition. (https://en.m.wikipedia.org/wiki/Dedekind_cut))

Defining the reals, however, is overkill when I suspect you all will be content to see why this should be the case. Essentially the problem that explains why numbers are defined so that 0.999... = 1 is that we want some quantity infinity such that

infinity + 1 = infinity

Or

infinity + r = infinity

Where r is a real number. This number is really important to define for questions like "what do all the numbers add up to?"

However, it follows directly from that desire that we should have

1/inf = 0

By definition; this is because we need to be able to take 1/r for r to be a real number and have it stay in the set of reals. 0 is a special case so it is okay to take 1/0 and end up outside the reals (in fact it is desirable). This is actually the interesting result - that we say 1/infinity is smaller than any real number that isn't 0, because it doesn't make any sense for something to be positive but smaller than 0. If any of you still believe this then you will see immediately that

1/inf + r = r

For any r.

There are sets of numbers where we don't use this rule, but that's not as standard. In those sets, 0.999... != 1, but you have to specify that that's what you mean and it comes at the price of the properties I outlined above.

[Anonymous No.10712248]

>>10711305

But you can't prove that every particle of Achilles makes it to the boundary, some particles will quantum tunnel in the opposite direction, therefore the total Achilles never reaches the finish line.

[Anonymous No.10712250]

>>10712240
>loop quantum gravity
Those far off positivist days of reading John Baez's blog just came back to me

[Anonymous No.10712253]

I don't know what's worse: Flat Earthers or people who don't think 0.999...=1

[Anonymous No.10712261]

>>10712235
2 = 1.999..., and every single person who's serious about math wouldn't disagree. The difference between 2 and 1.999... is typographic, but whether two is a (non-terminating) decimal depends on how you define decimal numbers. But whether 2 is non-terminating decimal doesn't matter, since determining which is the case is a matter of semantics; what matters is that 2 = 1.999...

[Anonymous No.10712264]

>>10712253
>he's a roundy

>>>/r/eddits thataway

[Anonymous No.10712269]

>>10712261
>the =fag, becoming desperate just repeatedly stutters his truism

I'll be here waiting for you when you have an argument buddy

[Anonymous No.10712270]

>>10712264

4chan used to raid the flat earth society, we've always been roundies.

[Anonymous No.10712271]

>it's a "/lit/ gets confused by high school math" thread
Stick to the books, nerds

[Anonymous No.10712280]

Anyone who believes 1 = 0.999... is a despicable post-modernists and likely Jewish

[Anonymous No.10712287]

>>10712271
to be fair, this isn't really high school math, more like "undergrad math major" math. People in my high school struggled with adding fractions.

[Anonymous No.10712291]

>>10712097
>-Infinite amounts of work are required to actually perform arithmetic
again, sounds like a meme

[Anonymous No.10712296]

>>10712102
the reals are a mathematical construct that has continuity, which doesn't work with discrete entities like atoms

[Anonymous No.10712298]

>>10712269
See >>10711231 and refute this pic

fucking idiot

[Anonymous No.10712301]

>>10712133
That's kind of the point. You can construct alternate number systems. Assuming the real system as canonical is default or 'actually real' is a philosophical bias. Otherwise, its a matter of admitting how the problem is formally stated relative to a given set of constructs.

You're at least not going to be able to prove that infinitesimals can't exist, which is the real essence of the problem when people debate the whole 0.999 = 1 thing.

[Anonymous No.10712302]

>>10712115
>Thousand years later it drove cantor insane
good

[Anonymous No.10712303]

>>10712291
Once this stupid meme is gone I don't care

[Anonymous No.10712305]

>>10712280
that fact has been understood for hundreds of years
it predates even the modernists, let alone the postmodernists

[Anonymous No.10712307]

>>10712298
>infinitely small numbers don't exist

Stopped reading there

[Anonymous No.10712308]

>>10712287
false
math undergrads do not struggle with these concepts; engineers and scientists (and especially undergrads in these fields) that never had to learn the rigid foundations do.

[Anonymous No.10712309]

>>10712140
>being autistic about real numbers
kek, what's the point? at that point just abandon mathematics and go full metaphysics

[Anonymous No.10712314]

>>10712305
So you're saying this is where things started to go downhill

[Anonymous No.10712317]

>>10712301
no the reason people debate this is because they are brainlets
when people who have not studied math think about numbers they want those numbers to have a number of properties they intuitively understand
the point is 0.999..=1 preserves all of those properties while the hyperreals break them left and right so those same retards are not thinking about those

[Anonymous No.10712318]

>>10712309
It's hilarious. Ok, so the real numbers can't be defined using Peano or ZFC or whatever the fuck you want. Just take them as an axiom then, they're too fucking useful to do otherwise.

[Anonymous No.10712320]

>>10712236
start with plato you fucking degenerate

[Anonymous No.10712321]

>>10712309
>at that point just abandon mathematics and go full metaphysics

Welcome to ascended tier

[Anonymous No.10712324]

>>10712307
The proofs in that pic don't depend on the assumption that infinitesimals don't exist. Refute the logic

[Anonymous No.10712336]

>>10712317
0.999..=1 isn't really relevant for the properties of the reals or whatever, it's just a simple result of the way we formally define decimal notation, which would otherwise be inconsistent.
you can just scrap the notation in its entirety and keep doing math happily.

[Anonymous No.10712341]

>>10712318
>axiomatics

[Anonymous No.10712347]

>>10712341
how autistic is this guy?

[Anonymous No.10712366]

>>10712347
quite

[Anonymous No.10712376]

>>10712341
Does he actually advocate mathematics without axioms? This is reaching levels of crankery that shouldn't be possible.

[Anonymous No.10712383]

>>10712376
How a man this nuts became an actual math professor I will never understand

[Anonymous No.10712392]

>>10712383
>>10712376
Oy vey he's questioning our holy torah, shut him down

[Anonymous No.10712393]

>>10712309
>implying mathematics wouldn't be better off without reals

[Anonymous No.10712406]

>>10711040
It's really easy to solve it mathematically. I guess it's a nice question though. It probably influenced Leibniz in some way. Newton was a fraud

[Anonymous No.10712410]

>>10712392
I assume most posting this don't understand the things he needs to deny to make this add up
Basic shit like the principle that two nonparallel lines must cross requires a master's degree to prove under his nonsense

[Anonymous No.10712412]

>>10712376
>>10712347
Lots of people have philosophies against set theory. One of the most famous instances of this is Lewis Caroll. (or Charles Dodgson as he was known to mathematicians). In his book Euclid and His Modern Rivals, he argues for a pedagogical curriculum centered around Euclid than anything else, and says that the criticisms of Euclid regarding parallel lines were invalid (common notion 5 and proposition 27 I believe). He never really addresses the criticisms of proposition one, but whatever those are more modern criticisms. I've addressed them before myself, it's a valid proposition.

There is a reason Euclid was the cornerstone of mathematical understanding for thousands of years. Just recently it has been taken out of the curriculum. They still teach it at some colleges. Same with On Conics, but much less colleges teach that, and when they do it's almost always just the first three books.

[Anonymous No.10712414]

The construct of mathematics is how we understand natural phenomena. Any mathematics that doesn't accurately represent the natural world is incorrect.

Zeno's paradox is simply wrong. There is no paradox. He is wrong. What he says is not the case.

>but mathematically...
I don't care.

If the maths says he's right the maths is wrong too.

[Anonymous No.10712415]

>>10712410
Well who said this shit had to be easy

[Anonymous No.10712417]

>>10712412
Sorry, it was postulate five, not common notion five.

Everything else is correct.

[Anonymous No.10712423]

>>10712415
There's a lot more to it
The idea that his way is more intuitive natural or logically sound just doesn't add up

[Anonymous No.10712427]

>>10712414
t. brainlet

[Anonymous No.10712429]

>>10712412
Non-Euclidean geometries predate set theory though.

[Anonymous No.10712431]

>>10712414
"models are wrong because they don't represent the real world in its entirety" the post

[Anonymous No.10712433]

>>10712423
Once the Jews don't win I'm happy

[Anonymous No.10712435]

>>10712427
>refusing to engage in my ivory tower sophistry of no relevance to anyone is "brainlet"
kek

>>10712431
Correct.

A model that doesn't represent the real world is inaccurate.

Translator's note: inaccurate means wrong.

[Anonymous No.10712439]

>>10712435
t. brainlet

[Anonymous No.10712441]

>>10712435
models only represent a part of reality per definition; they abstract many concepts.
by your nonsense, every model is wrong.

[Anonymous No.10712450]

Okay so in regards to Thompsons Lamp i've mulled it over and my best guess is that the light would be on

I havent read anything else, am I right?

[Anonymous No.10712452]

infinity is a spook anyway

[Anonymous No.10712458]

>>10712441
What is the purpose of making a model, anon?

Models are designed to allow us to make predictions. A model that doesn't help us do that is a pointless exercise in sophistry. Rather like OP's paradox.

Which was my fucking point.

This question is wank. It is prima facie wrong. It doesn't need to be explained why it's wrong because it's just fucking wrong. It would be like if I submitted to an architecture firm a design for a building with no ground floor. It would be a waste of everyone's time to even bother explaining to my why I was fired.

Kill yourself.

[Anonymous No.10712459]

>>10712431
>"models are wrong because they don't represent the real world in its entirety"

This sentence is 100% true though

[Anonymous No.10712464]

>>10712431
Why are you implying that statement is wrong?

Models ARE wrong, to greater or lesser extent. If they weren't they wouldn't be models.

[Anonymous No.10712465]

>>10712458
models are designed to allow us to make predictions about a part of reality, not its entirety

[Anonymous No.10712481]

>>10712465
>making a prediction about a part of reality isn't making a prediction about reality
>implying that the distinction, even if it exists, has any relevance to the argument anyway

The "muh turtle" paradox is a waste of everybody's time. It deserves as much attention as one of my farts.

"According to these maths, Achilles never overtakes the turtle!"
Wrong.
"BUT THE MATHS"
They're wrong too.
"BUT ACCORDING TO ALL THE MATHEMATICAL RULES MY MATHS ARE PERFECTLY CORRECT"
Then the rules are wrong.

I don't understand why it is so hard for you to realise that reality is never wrong. Anything that does not accurately represent reality is wrong. Full stop.

>but you can't explain WHY the rules are wrong
I don't need to.

There was some medieval scientist who spent his whole life weighing what he ate and what he shat out trying to figure out what exactly was happening in his body and why people needed to eat food. He never figured it out. But I tell you this - he still needed to fucking eat, even if he didn't know why.

[Anonymous No.10712490]

>>10712301
>Assuming the real system as canonical is default or 'actually real' is a philosophical bias

I never said that the real numbers were canonical. I said "canonical construction", i.e. the construction of the reals most commonly used in textbooks. There are other more exotic or complicated ways of constructing the reals, but they are STILL THE SAME REALS, i.e. they are exactly isomorphic.

>You're at least not going to be able to prove that infinitesimals can't exist,

They can exist, we can construct number systems where they exist. But those number systems lose many of the useful properties of the real numbers, and are generally a fucking pain to work with.

[Anonymous No.10712506]

>math is objective lmao
>almost 300 replies argumenting even the most basic shit

[Anonymous No.10712508]

>>10712459
>>10712464
i was mostly pointing out that op's statement is pointless, because any model would be wrong by his definition of wrong, i.e. any choice of axioms and all of mathematics is wrong, which is a pretty useless statement to make.

[Anonymous No.10712510]

>>10712481
the math dissolves Zeno's paradox though. if you do the math properly (i.e. with the ordinary real number system instead of the finitist meme math) the only price you have to pay in terms of intuition is a comparatively trivial one: some real numbers have more than one decimal representation.

i don't know why people get so fucking hung up on this -- they're willing to entertain such extravagant notions like infinitesimals and god knows what else. why is it so psychologically necessary that a real number have exactly one representation?

[Anonymous No.10712516]

>>10712510
Look, even if everyone is ok with R there's no guarantee that R is an exact model (oxymoron, btw) of the real world.

[Anonymous No.10712518]

>>10712506
That's because there are a lot of brainlets here that are just wrong

[Anonymous No.10712521]

>>10712308

Not our fault they don't teach rigorous math, we don't determine the school policy.

[Anonymous No.10712533]

>>10712516
it's the best one we have. zeno's paradox becomes nonsensical on a purely physical level past a certain point anyway; quantum uncertainty means you can't measure achilles' and the tortoise's positions with complete accuracy.

all this does is lower my opinion of philosophers. basically "it works in practice, but does it work in theory?"

[Anonymous No.10712545]

>>10712516
R clearly is NOT an accurate measure of the real world. You can't define a measure on all of R^3, but I'm pretty sure all volumes are defined in real space. Any physicists that can weigh in on this?

[Anonymous No.10712546]

>>10712510
It still requires passing through infinite time and space whether you can represent it mathematically or not. This is a problem

[Anonymous No.10712554]

>>10712545
what do you mean you can't define a measure on all of R^3? don't you mean you can't define a uniform measure? that's true (and also true in R) but I don't see what it has to do with volumes in physical space.

[Anonymous No.10712557]

>>10712546
no it isn't, learn how convergence works.

[Anonymous No.10712564]

>>10712521
well, anybody that makes bold claims about mathematics while not having studied the rigorous foundations himself is an ignorant twat, at least.

[Anonymous No.10712569]

>>10712533
>all this does is lower my opinion of philosophers.
If your opinion of """""philosophers""""" isn't already zero you're not thinking hard enough.

No philosopher has ever made life better for anyone. At my most generous the maximum I could possibly allow is that philosophers might have provided some clarity for the great men who actually implemented ideologies, but I doubt it.

If every person who ever actually made a living from "being a philosopher" never existed I think the world would turn out pretty much exactly the same as it has. They're a bunch of cloistered ivory tower faggots.

[Anonymous No.10712579]

>>10712569
we /b/ now?

[Anonymous No.10712584]

>>10712554
If R^3 was an accurate model of our space then we wouldn't be able to construct an unmeasurable set

[Anonymous No.10712587]

>>10712579
I wasn't an anti-intellectual until I had to suffer through them at university.

[Anonymous No.10712589]

>>10712518
Post your thesis

[Anonymous No.10712592]

>>10712587
t. engineer or natural science brainlet

[Anonymous No.10712594]

>>10712557
Convergence is literally the act of combining infinite quantities. Even if they get regressively smaller one still has to experience each fraction

Again stop mistaking functional abstraction with reality

[Anonymous No.10712608]

>>10712592
Actually I studied Political Science and took philosophy electives.

When I asked someone in my first year "but where is the proof?" they basically straight up admitted there is none, and that all philosophy is based on making shit up based on assumed "axioms." You pick things that you want to be true and then pretend that they are, and hey presto, you're a philosopher.

I asked every other lecturer I had after that the same question and never got a more satisfactory answer.

Thus I became a positivist.

And you literally cannot prove that I'm wrong.

[Anonymous No.10712615]

>>10712584
Evidence that the axiom of choice is wrong.

[Anonymous No.10712620]

>>10712594
convergence is a declarative statement, it isn't an act (also, i'm sure you want "infinitely many" instead of "infinite")
just because you traverse through infinitely many points in space does not mean that you traverse through infinite time or infinite space

[Anonymous No.10712633]

>>10712620
>just because you traverse through infinitely many points in space does not mean that you traverse through infinite time or infinite space

Which still leaves the problem totally unresolved
Calculus has zero relevance on this subject

[Anonymous No.10712642]

>>10712608
yes, you don't prove axioms, boo fucking hoo
what's your suggested alternative?

>>10712615
both the lack and the use of aoc yield unintuitive results

[Anonymous No.10712647]

>>10712642
>what's your suggested alternative?
Refraining from wasting everyone's time with pointless wank.

If you don't prove your axiom I have no reason to accept it and your entire exercise in """philosophy""" collapses.

So fuck off.

[Anonymous No.10712656]

>>10712584
I don't really understand your point. What unmeasurable sets do we encounter in physics?

[Anonymous No.10712663]

>>10712647
You can't prove an axiom, that's the whole fucking point, you need to assume SOMETHING to get anywhere. Even your meme philosophy is based on assumptions, whether you admit it or not.

[Anonymous No.10712664]

>>10712647
>Refraining from wasting everyone's time with pointless wank.

the only waste of time is this entire discussion.

[Anonymous No.10712670]

>>10712656
We don't, that's my point. If I can construct something in R^3 that can't exist in reality, then R^3 is not an accurate model of reality.

[Anonymous No.10712674]

>>10712633
>It still requires passing through infinite time and space whether you can represent it mathematically or not. This is a problem
>just because you traverse through infinitely many points in space does not mean that you traverse through infinite time or infinite space
>Which still leaves the problem totally unresolved

>it still requires foo. this is a problem
>foo is not a thing
>problem still unresolved
???

>>10712647
>here's a hammer, it's pretty useful in a bunch of scenarios where the axioms for the use of the hammer are fulfilled
>if you can't prove those axioms then I have no reason to accept your hammer, fuck off!

[Anonymous No.10712675]

>>10712663
>you need to assume SOMETHING to get anywhere
No you don't.

Your mistake is in thinking that it's possible to get anywhere without being able to prove how you got there.

Your philosophy, no matter how ironclad the reasoning, is a castle built on sand. It is utterly fucking worthless because the entire basis is "because I said so."

Well fuck off. I don't accept that. And now you're helpless. You literally can't do a fucking thing in response. I don't accept your axiom, so get back up on your horse and tell your story walking pal.

See now how philosophy is a waste of time? The most impassioned and impenetrable argument can be thoroughly defeated with the debate equivalent of "nuh uh, fuck off."

You'd be better served learning how to use a gun.

[Anonymous No.10712678]

>>10712670
You don't even need measure theory for such a trivial observation -- pi doesn't exist in reality either but it's in R. Who the fuck cares?

[Anonymous No.10712682]

>>10712674
>>here's a hammer, it's pretty useful in a bunch of scenarios where the axioms for the use of the hammer are fulfilled
>>if you can't prove those axioms then I have no reason to accept your hammer, fuck off!
"Here's a hammer. Here's 6 millenia worth of observational evidence that you can use it to hammer nails."

as opposed to

"Here's a hammer. I assume that it can be used to fly. I can't prove that but hey, we've gotta assume something to get anywhere, right?"

[Anonymous No.10712690]

>>10712674
How can one ever complete a transition through infinite points?
All that calculus allows us to do is quantify processes that occur in limited spaces, it has nothing to do with experience

[Anonymous No.10712702]

>>10712682
yes, intuitive motivations for axioms are often not taught, but they do exist, and the more you learn about mathematics, the more you realize why we assume certain things.
it's not like people just come up with this shit by random chance, it's still the result of observational evidence (that has no rigid proof).

[Anonymous No.10712705]

>>10712690
because each time interval goes to zero fast enough that it converges to a finite number.

[Anonymous No.10712714]

>>10712608

[Anonymous No.10712720]

>>10712678
pi as the circle constant certainly exists in reality, though I suppose you could argue a "circle" can't be realized.

>Who the fuck cares?
The mathematical empiricists in this thread. I don't care personally.

[Anonymous No.10712724]

>>10712702
>observational evidence (that has no rigid proof).
Observational evidence was a bad example because of course we can't prove that our senses and perceptions are correct.

My point is that observation forms the exclusive basis of all knowledge. We observe achilles overtake the tortoise. We don't observe achilles getting stuck in infinite division. Thus any sophist posturing about muh infinite division is pointless timewasting in the face of direct observation.

>"but how do you know your senses are right"
It doesn't matter if they're objectively right. So long as they are consistent and predictable they're good enough for me to live my life.

There's a whole world of sensation denied to the blind but they don't implode in on themselves because they're unable to fully appreciate existence.

[Anonymous No.10712800]

>>10712724
choosing a rigid foundation is helpful.
it's a common ground for what you're working on.
it eliminates arguments that spawn from people believing in different things.
it also helps with reducing or abstracting the complexity of some topic, meaning that you can use it more efficiently.

no rigid foundation is perfect. different foundations have different trade-offs: assuming certain axioms may help with expressibility in one area, while assuming others may help with expressibility in another one, while not assuming certain axioms may help with things like computability.

if you make an observation that doesn't really fit into one of your foundations (and expressing that observation is important), you come up with a new one.
this doesn't mean that the other foundations are wrong; they just choose different trade-offs and are more efficient in other areas.

[Anonymous No.10713029]

>>10712682
>"Here's a hammer. I assume that it can be used to fly. I can't prove that but hey, we've gotta assume something to get anywhere, right?"
A hammer evidently cannot fly.

Take Euclidean geometry, for example. Do you think Euclid's axioms and postulates should be tossed out, even though they're pretty much self-evident? How could you prove the Pythagorean theorem, for example, if you have no starting point? Do you propose that we do away with axioms all together in favor of empirical methods? Should we measure the hypotenuse of every right triangle just to be sure? Fucking retard

[Anonymous No.10713067]

>>10713029
>Do you think Euclid's axioms and postulates should be tossed out
they're unrigorous, see hilbert's axioms

[Anonymous No.10713082]

>You might think every number has a unique decimal expanson.
Depends on the type of number.
>A simple proof by induction:
This relies upon being able to calculate 10*0.99... Under some ways of thinking about it such a computation would not terminate. Therefore, 10*0.999... does not necessarily equal 10x.
>An appeal to intuition
Water is quantized.
>Define 0.999... as
Suppose I don't define it that way.

Ultimately this all depends on your definitions and axioms. It is not the case that 0.999... = 1 but that under a very common formalization of the real numbers that it does and this formalization seems to closely model many aspects of our physical reality.

[Anonymous No.10713093]

>>10713067
Ok I'm assuming you're not him. I mentioned Euclid's axioms for the sake of simplicity

[Anonymous No.10713177]

>>10711327
>t than the common logic/word paradox ("This a lie".... etc ).
https://en.wikipedia.org/wiki/Hilbert%27s_program
No system has unrestricted self-reference and is complete and consistent. This is a real and actual paradox. In contrast the situations in Plato's paradoxes can be consistently described and calculated.
>>10711628
"Why" is ultimately irrelevant. All we can do is describe "how" in a consistent way. You can always have an infinite regress of asking "why."
>>10712608
Assuming empirical reality and not solipsism is an axiom too anon.
>>10712584
Can't you just "toss out" the unmeasurable subsets of R^3 or something? Just ban Gabriel's Horn and such?

[Anonymous No.10713228]

>>10713177
>Can't you just "toss out" the unmeasurable subsets of R^3 or something?
With the Axiom of Determinacy you won't have em. Can't have Axiom of Choice then, tho.

[Anonymous No.10713445]

>>10713082
>a very common formalization of the real numbers
Are you retarded or 10 years old? The real numbers are defined as follows:

Let R denote the set of real numbers, then the following holds.
1. R is a field
2. There is a total order on R that is compatible with addition and multiplication.
3. R is Dedekind complete, that is every sub set S of R that is bounded above has a least upper bound.

If any of these fails, it is NOT the real numbers.

[Anonymous No.10713495]

funniest thread i have seen in this board

[Anonymous No.10713542]

>>10713445
anon, he doesn't even understand that the decimal notation is independent from the definition of the reals, there's no point

[Anonymous No.10713777]

> ITT mathlets

[Anonymous No.10713793]

As delta X approaches infinity, so does delta Y

You cross smaller lengths of space but you do so in smaller lengths of time