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/sci/ - Science & Math

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12757950 No.12757950 [Reply] [Original]

lim n -> infinity 2^n - 1 > 0 edition

>> No.12757954

1/inf=0

>> No.12758001

>>12757954
1/inf = 0+
1/(-inf) = 0-

>> No.12758057
File: 149 KB, 956x901, Science.png [View same] [iqdb] [saucenao] [google]
12758057

>>12757950
Pic related.

>> No.12758222

>>12757954
0/inf = 0.
0 is different from 1.

>> No.12758223

>>12758222
0/inf = 1/inf = 0

>> No.12758263

>Truth is what matters most, not "common semantic value"
"Truth" of what? That's your problem, it seems. You seem to be on some sort of mystical jihad for "truth," but you don't even know the common semantic value of the words and symbols you're using to try to and convey your "truth."

>> No.12758268

>>12757950
OP's brain does not exist.

>> No.12758270

>>12758057
Also you fucked up your base-20 lettering system again.

>> No.12758277

What is [math]\frac{1-0.999...}{2}[/math]?

>> No.12758288

>>12758277
oh is this a pemdas thread now, too?
one minus one is zero; zero divided by two is zero

>> No.12758297

>>12758057
Even by the usual lame shitpost standards set by /sci/ that is laughable.

>> No.12758307

>>12758222
r/inf=0

>> No.12758310

>>12758001
0-=0=0+

>> No.12758317

>>12758277
Obviously 1-0.9945...

>> No.12758319

>>12758268
[math] \displaystyle
\lim_{n \to \infty} 2^n - 1 = \infty -1 = \infty
[/math]
perfectly ok

>> No.12758326

>>12758263
I mean you're the one saying "open neighborhood" is a non-standard term. dunning–kruger at its best.

>> No.12758331

Infinity is a number greater than any number mankind can imagine.
Taking away the number propriety of infinity takes away all meaning from it.
infinity > any positive number you imagine.
-infinity < any negative number you imagine.
0/infinity = 0. Infinity is still a number and can occasionally be used, like in this case.
Operations between infinities cannot be used in the case of opposites operation, like infinity - infinity and infinity / infinity,
but for things like 0xinfinity and 0 / infinity, it certainly can. Both answers yield 0.
lim z->infinity(1/z) = 0+, the + is here to show you that no matter what y > 0 you can think of, y > 0+ > 0.
lim z->infinity(-1/z) = 0-, the - is here to show you that no matter what y < 0 you can think of, y < 0- < 0.
Simple.

>> No.12758344

>Infinity is a number

Four words that suffice to stop reading right there.

>> No.12758346

>>12758326
Oh, I get it now. You're like a boy who reads a popular science about black holes and then uses the term "event horizon" as a metaphor to describe something else. Stick to your donuts and coffee cups, boy.

>> No.12758358

>>12758346
>I have no argument

>> No.12758360

>>12758358
You don't need to greentext that.

>> No.12758363

>>12758331
>Infinity is a number
wrong

>> No.12758366

>>12758360
you have no argument
like this?

>> No.12758375

>>12758366
No, you can greentext that one.

>> No.12758402

>>12758375
retard

>> No.12758403

>>12758375
>you have no argument
[math]\lim_{n \to \infty} n = \infty[/math], deal with it

>> No.12758413

>>12758403
How to deal with it other than pointing out that the RHS is undefined,
and the expression is syntactically invalid?

>> No.12758417

>>12758403
No one disputes that, torus boy.

>> No.12758419

>>12758417
It is hard to dispute when it makes no sense.

>> No.12758424

You fucking idiots keep arguing this because both sides are right in their interpretation

0.9999... DOES NOT EQUAL 1

lim(0.9999...) EQUALS ONE

>> No.12758437

>>12758424
0.999... = limit (0.9, 0.99, 0.999,...) = 1

>> No.12758444

>>12757950
The limit does not exist. There is no number to which that sequence gets arbitrarily close.

>mub topological space
>muh neighborhood
Has nothing to do with the limit of a sequence.

>> No.12758451

>>12758424
>0.9999... DOES NOT EQUAL 1
0.9999... can't be any different than 1 unless you invent a new "truth" about the common semantic value of the ellipsis (as a symbol used in decimal representation), which is that a specified pattern of digits doesn't end.

>> No.12758461

>>12758413
[math]\mathbb{N} \cup \{ \infty\}[/math] and [math][-\infty,\infty] = \mathbb{R} \cup \{ -\infty,\infty\}[/math] are topological spaces, so limits make perfect sense here. what's so confusing?

>> No.12758484

>>12758444
>>mub topological space
>>muh neighborhood
>Has nothing to do with the limit of a sequence.
actually it has everything to do with the limit of a sequence

"for every ε>0 there exists N such that n>N implies |a_n - L| < ε"

is the same as

"for every set in the form (L-ε,L+ε) there exists a set in the form (N,∞) such that n ∈ (N,∞), implies a_n ∈ (L-ε,L+ε)"

which is the same as

"for every open set V containing L there exists an open set U containing ∞ such that n ∈ U, n ≠ ∞, implies a_n ∈ V"

>> No.12758485

>>12758461
Wow that's so cool. Have you read any popular science articles about quantum mechanics yet? What can wave functions tell us about 0.999...?

>> No.12758509

>>12758484
Lol. Here's where your third equivalency fails.
>containing ∞

>> No.12758511

>>12758461
Nothing is confusing. We knew from the get go that you have no clue about the concepts of
topology or limits, and this keep getting confirmed.

>> No.12758531

>>12758511
all, right what exactly do you have a problem with?

>>12758509
(K,∞] contains ∞, you're claiming otherwise?

>> No.12758590

>>12758531
No, I'm pointing out why your "equivalency" fails. You're trying to retrofit ∞, as an element included in one setting, into different setting which excludes it by definition.

>> No.12758597

>>12758485
>i have no argument

>> No.12758603

>>12758597
You don't need to greentext that.

>> No.12758614

>>12758603
>tourist
go back

>> No.12758635

>>12758590
Limit of a sequence fits into the general setting of limits of maps between topological spaces if you include inf into natural numbers and equip it with the order topology. numerical sequence diverging towards inf fits into the general setting of limits of maps between topological spaces if you include inf into real numbers and equip it with the order topology. such sequence doesn't have a limit in R but it does in [-inf,inf]. what exactly do you have problem with?

>> No.12758659

>>12758614
>retard
A poster with no argument, writes "I have no argument." That's a simple declarative sentence. You don't greentext that, imbecile.

>> No.12758665

>>12758635
Wow cool, but you still haven't explained how black holes fit into your theory. What about the Dirac delta, can we find a way to use that, too?

>> No.12758678

>>12758635
>such sequence doesn't have a limit in R
that's the point dumbfuck

>> No.12758730

>>12758635
Wtf is "order topology on the natural numbers"?

>> No.12758772

>>12758659
>i'm pretending to know something
you're not the first one

>> No.12758775

>>12758730
It's exactly like the wave function collapse that decomposes rational primes === 1 (mod 4) in Q(√-1) which we can also use to collapse the event horizon of N and prove the truth.

>> No.12758779

>>12758772
You keep greentexting your declarative sentences, retard.

>> No.12758781

>>12758775
I'm guessing you believe in quantum consciousness? You're using the same babble they do.

>> No.12758818

>>12758781
No, I'm agreeing with and amplifying OP's mishmash of math jargon, in the hope that it helps him understand how his argument sounds to everyone else.

>> No.12758854

>>12758779
lol, you're clueless on how greentext works
go back to tik tok

>> No.12758859

>>12758854
Are you drunk, or just stupid?

>> No.12758863

>>12758859
>i'm sooo smart
newbie
>fucking idiot

>> No.12758864

>>12758859
>I'm a newfag
lurk moar

>> No.12758869

>>12758863
>>12758864
I'm guessing you're just stupid.

>> No.12758886

>>12758484
>is the same as
No, it's not. One has to do with being arbitrarily close to the limit, and the other does not.

>> No.12758993

>>12758730
order topology on N is just the discrete topology
order topology on N ∪ {∞} is discrete with the exception of ∞ whose open neihgborhoods are the sets {n, n+1, n+2,...,∞}
https://en.wikipedia.org/wiki/Total_order
https://en.wikipedia.org/wiki/Order_topology

>>12758678
I have never claimed otherwise, dumbfuck

>>12758886
a convergent sequence (that is convergent in R) is getting closer to its limits in the exact same sense in which a sequence growing beyond all lower bounds is getting closer to ∞ in [-∞,∞].

>>12758665
this is not "my theory" you sad brainlet, this is what every math student who has taken a course on general topology knows. it's explained even on wikipedia, lol.

>> No.12759008

>>12758993
>its limits
*limit

>> No.12759081

>>12758993
>this is not "my theory" you sad brainlet, this is what every math student who has taken a course on general topology knows.
Right. Feel free to cite any "general topology" textbook that conflates topology with calculus.

Oh, you can't? Guess it's "your theory" after all, isn't it.

>> No.12759106 [DELETED] 

>>12758993
a convergent sequence (that is convergent in R) is getting closer to its limits in the exact same sense in which a sequence growing beyond all lower bounds is getting closer to ∞ in [-∞,∞].
which, again, has sweet fuck all do with whether or not a sequence has a limit in R

>> No.12759113

>>12758993
>a convergent sequence (that is convergent in R) is getting closer to its limits in the exact same sense in which a sequence growing beyond all lower bounds is getting closer to ∞ in [-∞,∞].
which, again, has sweet fuck all do with whether or not a sequence has a limit in R

>> No.12759211

>>12758993
>a convergent sequence (that is convergent in R) is getting closer to its limits in the exact same sense in which a sequence growing beyond all lower bounds is getting closer to ∞ in [-∞,∞].
No, they're completely different. The sequence doesn't get closer to ∞ at all. It remains infinitely far away even as it grows without bound.

>> No.12759294

>>12758363
Suppose infinity is a symbol.
Why, then, can you do things like infinity + 1 = infinity and 5/infinity = 0?
Sure, you can do things like normie + diploma = pain.
But those do not mix with numbers unless you do things like result + 0 = failure, which has no place in maths.
On the other hand, treat infinity as a number greater than any number you can imagine and the 1+infinity=infinity, 1-infinity=-infinity, 5xinfinity=infinity makes sense.
Some operations are illegal, like infinity-infinity; but 0 also is a number that cannot divide anything.
Infinity is a number greater than anything humans have conceived, yet was deemed a symbol out of mankind arrogance thinking that no number was too great for them.
The so-called infinite space and time is not infinite, mankind is just too arrogant to admit some things are beyond them.
Infinity is a number greater than any number mankind can imagine.

>> No.12759375

>>12759081
all of them. it's impossible to not "conflate" topology with calculus, because topology is the basis for real analysis. calculus starts at limits and continuity. both are literally topological concepts. but if you absolutely want a concrete example, rudin or pugh. while not books on general topology per se, they do explain basic topological terms and their relation to calculus.

>>12759113
>which, again, has sweet fuck all do with whether or not a sequence has a limit in R
I've never claimed that a sequence such as 2^n has a limit in R, I've been saying it has a limit in [-∞,∞] from the get-go. it's also unrelated, that was a response to the claim that a sequence cannot get "closer" to ∞ which is just plain false, see below.

>>12759211
>The sequence doesn't get closer to ∞ at all. It remains infinitely far away even as it grows without bound.
you're just saying that if you try to extend the ε,δ-definition to the extended reals, it doesn't work. that's of course true, because the extended reals are not a metric space in the first place. the metric on R cannot be extended to [-∞,∞], because the distance between ∞ and every real number would have to be infinite and you would get the false impression that one cannot get closer to ∞. but you don't need a metric to talk about limits, or even "getting closer" to something, you just need to know what open sets are. limits and continuity are topological concepts, they're far more general than what you learn in calculus. a mapping has limit L at p if for every open set V containing L there exists an open set U containig p which is mapped into V. in metric spaces (such as R) this is the same as the ε,δ-definition, but that's just a special case. I can give you many more examples of metric spaces which make perfect sense as being embedded inside larger spaces which are not metric spaces anymore, only topological.

>> No.12759378

>>12759211
I mean if you can't see that

[math]\lim_{n\to\infty}a_n = L[/math] iff [math]a_n[/math] is eventually in every [math](L-\epsilon,L+\epsilon)[/math]
[math]\lim_{n\to\infty}a_n = \infty[/math] iff [math]a_n[/math] is eventually in every [math](K,\infty][/math]

is the exact same thing conceptually, I don't know what else to say.

>> No.12759385

>>12759378
[math]\lim_{n\to\infty}a_n = L[/math] iff [math]a_n[/math] is eventually in every [math](L-\epsilon,L+\epsilon)[/math]

[math]\lim_{n\to\infty}a_n = \infty[/math] iff [math]a_n[/math] is eventually in every [math](K,\infty][/math]

>> No.12759392

>>12759378
>>12759385
last attempt
[math]\lim_{n\to\infty}a_n = L[/math] iff [math]a_n[/math] is eventually in every [math](L-\epsilon,L+\epsilon)[/math]
and
[math]\lim_{n\to\infty}a_n = \infty[/math] iff [math]a_n[/math] is eventually in every [math](K,\infty][/math]

>> No.12759406

>>12759375
>you're just saying that if you try to extend the ε,δ-definition to the extended reals, it doesn't work.
No, it works perfectly well. What doesn't work is infinity being a limit to a sequence that doesn't get close to infinity.

>> No.12759413

>>12759294
You have it backward. It's even more arrogant to imagine that infinity is some sort of unimaginable maximum. Why should it have a limit? Why should there be a maximum number? Is it because you're too arrogant (or existentially ill-at-ease?) to admit that there might not be a limit to some things?

>> No.12759421

>>12759375
>all of them.
As I expected, you can't. Name dropping Rudin isn't a citation.

>> No.12759432

>>12759406
can you please write down the exact meaning of
[eqn]\lim_{n\to\infty} a_n = \infty[/eqn]
or
[eqn]\lim_{x\to x_0} f(x) = \infty[/eqn]
you were (hopefully) taught in your calculus or analysis class?

>> No.12759464

>>12759421
what exactly do you mean by "conflate calculus with topology" then? both books introduce basic topology, then use topology to define continuity and limits, then use continuity and limits to build calculus. did you want something else?

>> No.12759471

>>12759378
You're a mess. (K,∞] will never be a valid construction in R no matter how many different latex formulas you write out.

It's like you're trying to prove that n^2+1 has a solution in R because it has a solution in C, and C is conceptually similar to R. That doesn't matter. n^2+1 will never have a solution in R, and a sequence that grows without bound will never approach any limit in R.

>> No.12759532

>>12759464
I asked you to cite where in your "general topology textbook" / "even on wikipedia, lol" it tells you that lim n->∞ (2^n-1)/(20^n) converges to anything other than 0.

>> No.12759565

>>12759432
Infinity isn't a limit. Whatever meaning is nominally ascribed to those forms is irrelevant.

>> No.12759567

>>12759471
[-∞,∞] is not a construction *IN* R, it is a topological and algebraic extension of R to make several things more unified, definitions and calulations of limits in particular. (K,∞] is not a subset of R, but it's subset of [-∞,∞]. your analogy fails, because I'm not trying to "prove" that a sequence such as 2^n has a limit in R. it doesn't, but it does in [-∞,∞]. for the tenth time already, I haven't claimed anything else.

>>12759532
firstly, you didn't. secondly I'm not claiming that lim n->∞ (2^n-1)/(20^n) is non-zero. that's OP, and I'm not OP.

>> No.12759589

>>12759565
it's very relevant, because this meaning 100% agrees with the construction I'm describing. you think this is a coincidence?

>> No.12759602

>>12759589
>it's very relevant, because this meaning 100% agrees with the construction I'm describing.
Why would I care what some nominal description agrees with?

>> No.12759638

>>12759589
Your argument is akin to saying a divergent series converges because Cesaro summation looks like standard summation.

>> No.12759641

>>12759602
because you're obviously having some problem with the extended real numbers, in particular with the fact that a sequence can have a limit equal to ∞ here. this exact same thing is taught in baby calculus, it's just phrased differently, so that it would be digestible for people who don't know topology yet.

>> No.12759656

>>12759567
>firstly, you didn't.
Of course I did. Read the thread. What on earth do you think we're talking about? If your babbling isn't responsive to the thread, what point are you even trying to make?
>I haven't claimed anything else.
Then who cares? Are you just posting random thoughts like a diary? Are you playing out some weird remedial math tutor fantasy? If so, you definitely need more practice.

>> No.12759664

>>12758057
Stop being retarded enough to believe this garbage.

>> No.12759665

>>12758057
[math]\lim\limits_{n \to \infty} \left( \dfrac{2^n - 1}{20^n} \right) > 0[/math]

Hahaha.

>> No.12759688

>>12759665
2^n - 1 > 0 if n > 0
20^n > 0 if n > 0
lim n∞((2^n - 1)/(20^n))=0+>0

>> No.12759710

>>12759688
You're either trolling or have no idea how limits work.

>> No.12759716

>>12759688
0+ = 0
lim n∞((2^n - 1)/(20^n))=0

>> No.12759741

>>12759688
If 0+ > 0, then 0- < 0.
lim n -> infty (1/n) = 0+
lim n-> -infty (1/n) = 0-
lim n-> infty (1/n^2) = lim n-> -infty (1/n^2) = 0

But 1/n^2 < 1/n for all |n| > 0. So how do you propose that

lim n -> infty (1/n^2) > lim n -> infty (1/n)

if 1/n^2 < 1/n for all n > 1?

>> No.12759787

>>12759656
My whole point is (and has been for a few days) that lim a_n = inf is a valid statement, and that it contains more information than simply saying "the limit does not exist". Read the previous thread.

>> No.12759801

The + in 0+ doesn't change the number value of 0. It's a different information, like you are 0 meters in front of a wall and also moving at 100 km/h toward the wall.

>> No.12759811

>>12759787
Can you link previous thread? I'm interested

>> No.12759901

>>12759787
You must be quite inept at expressing yourself if you've convinced people to disagree with the tautological statement that the limit of a sequence which goes to infinity is infinity. For days on end, no less.

Based on what you've written in this thread, however, I think it's likely that no one is disagreeing with your pointless tautology, but rather with the extraneous, flawed conclusions you keep trying to draw from that tautology, while pretending not to.

>> No.12760043

>>12758424
>lim(0.9999...)
dafuq does this even mean ...

>> No.12760167

>>12759901
>extraneous, flawed conclusions
such as?

>> No.12760203

Man I can't wait for Pi to increase and math and science and physics fags to have mental breakdowns and commit sudoku.

>> No.12760298

>>12760203
I'd be likely to piss myself in excitement than have a breakdown. I'd be asking how can the limit of a series suddenly change.

>> No.12760348

>>12759741
lim n-> infty (1/n^2) =0+
lim n-> -infty (1/n^2) =0+
(sign of n does not matter in the case of n^2)

Let's continue.
lim n -> infty (1/n^2) = lim n -> infty (1/n) = 0+
obviously 1/n^2 < 1/n for every n > 1.
Still, they both have the same limit.

>> No.12760355

>>12759716
every positive number you can think of > 0+ > 0 > 0- > every negative number you can think of

>> No.12760394

>>12759413
False.
For the arrogant modern scientist, infinity is a symbol, something unnatural.
For the less arrogant, infinity is a number greater than any number mankind can think of. Infinity is a perfect illusion, an illusion that rose from pride, anger, intellectual spite of the spiritual. Infinity cannot exist. Everything has a beginning and an end.
Those who believe infinity is no number (while acting like hypocrites and using it like one at times) are wrong.
Infinity is a number greater than any number mankind can imagine, and the word was born out of the ignorance of someone who does not know all and assumes all things unknown are "infinite".

>> No.12760423

>>12760167
You tell me. You’ve apparently been arguing for days about a simple tautology, which I’ve never seen anyone dispute. Summarize one argument that’s been made against your “whole point.”

>> No.12760461

>>12760394
False. It’s the height of arrogance to assume that everything has a beginning and an end, simply because of what mankind can or can’t imagine, or what you imagine mankind can’t imagine.

>> No.12760679

INFINITY IS NOT A NUMBER
The infinite decimal expansion of 0.999... = 1. Only finite decimal expansions of 0.999... < 1.

>> No.12760795

>>12760355
+ and - measure something different. see >>12759801

>> No.12760830

>>12760461
False.
It is arrogant of you to make wild claims about there being no beginning and end.
You have yet to tell me of one single thing that has neither beginning nor end.
Life and Death. Beginning and End. The Natural order triumphs over your lies.

>>12760795
0+ is positive, 0- is negative.

>> No.12760837

>>12760461
You are being very arrogant in saying no number is too great for mankind.
Some numbers, like infinity, are beyond the scope of men.

>> No.12760866

>>12760830
>wild claims about there being no beginning and end
I'm not claiming that. You're claiming that it's impossible because you can't imagine it, and because you can't imagine an imaginary group of imaginations you call "mankind" imagining it. I'm just pointing out the arrogance of your imagination.

>0+ is positive, 0- is negative.
0 is the absence of a sign, so neither of the things that you're thinking about when you describe 0+ and 0- have anything to do with 0.

>> No.12760875

>>12760837
I've never said that. I've said that your attempt to anthropomorphize everything into a number that must have a beginning and an end is the most arrogant thing imaginable. Shame on you.

>> No.12760948

>>12759641
>because you're obviously having some problem with the extended real numbers, in particular with the fact that a sequence can have a limit equal to ∞ here.
Yes, the problem is that it's not a limit.

>> No.12761376

>>12760423
>>12743276

>> No.12762323

>>12760866
You are free not to believe in 0+ and 0-, just like I am free not to believe 1+1=2.
In that case, you should not lecture me.

>>12760875
Failure, show me one single thing that has neither beginning nor end.
Since you cannot, everything in this world has a beginning and an end, until proven otherwise.
You are full of absurd beliefs, pal.

>> No.12762324
File: 2.38 MB, 1468x7317, lemmings.png [View same] [iqdb] [saucenao] [google]
12762324

>>12760875
The harshest truths are the one that will do you the most good.

>> No.12762336

>>12760830
>You have yet to tell me of one single thing that has neither beginning nor end.
the open interval (0,1)

>> No.12762342

study hyperreals fags

>> No.12762345

>>12762323
Where did the sun begin?
Where did your parents begin?
Seems like you are taking inputs on faith from some groups and not others.
Nothing is trusted and your argument is rendered invalid because most everything has unaccounted beginnings and endings. Does that person you saw at the store actually die? Why do you think so?

>> No.12762434

>>12761376
You don't need to use sets that don't exist in R to explain why lim = ∞ contains more information than lim dne. Just compare 2^n to (-2)^n, for example.

>> No.12762442

>>12762323
>You are full of absurd beliefs, pal.
Name one. So far, you're the only one who has claimed to believe in the certainty of things you can't imagine. Look in a mirror, pal. You're brimming up to your eyeballs in arrogance, and all the arrogance you've described so far in others is, in fact, your own.

>> No.12762718
File: 363 KB, 1080x739, 1611826958315.png [View same] [iqdb] [saucenao] [google]
12762718

>>12762345
God.

>>12762442
False, your no u arguments are utter failure.
Learning your lessons and having good grades makes you no more than a dog who can do magic tricks.

>> No.12762725

>>12762442
Funny, I acknowledge infinity as a number too great for men to grasp, and I am the arrogant one?
You and your scientists friends are so full of pride, refusing to admit that no number is too great for you that you have lost touch with reality.

>> No.12762771

>>12762725
You are the one who refuses to acknowledge that there are limits to what you can and can't know.
You continue to argue from your own blindness.
You have never seen a thing with no beginning or end, and simply because you, a human, has never seen such a thing, you have the remarkable arrogance to assume that such a thing can't exist. And you continue to bleat out your arrogant assumption, over and over again, like a silly sheep.

>> No.12763842

1+1=1, anyone?

>> No.12763846

>>12762771
Yes I have seen many things die and many things born. Everything has a beginning and an end.
You have yet to tell me a single thing that has neither beginning nor end.

>> No.12763887

>>12762771
Don't you think you being born and eventually dying constitutes a beginning and an end pal?

>> No.12763959 [DELETED] 

>>12763846
Look at you, acting as if you have the eyes of God and can see everything. Speaking in absolutes, as if your quick, mortal experience gives you stature to pass judgment on the alpha and omega of the universe. Pathetic.

>> No.12763963

>>12763846
>>12763887
Look at you, acting as if you have the eyes of God and can see everything. Speaking in absolutes, as if your quick, mortal experience gives you stature to pass judgment on the alpha and omega of the universe. Pathetic.

>> No.12764015

>>12763842
The binary operation described is not addition, but rather
[math]A\,\oplus\,B\;=\;\big[\,clay\in(A\,\cup\,B)\,\big][/math]
where [ ] is the Iverson bracket.

>> No.12764203

>>12763963
I speak truth, you come from a daddy and a mommy.
You are being constantly unsure of everything. If you doubt yourself, that means what you believe in is a lie. If I am sure of what I say, that means I tell the truth.
There is a beginning and an end to all in this world.

>>12764015
Nope, it is an addition, that is what heppens when you ADD two lumps of clay together. Feel free to play semantics all you want, but 1+1 = 1 in the case of clay.
It is no UNION, unlike when you UNITE a man and a woman under the same law. The two elements remain separate.
1+1 = 2 in the case of clay.

>> No.12764323

>>12764203
>I speak truth
>I am sure of what I say
>I tell the truth
>There is a beginning and an end to all in this world
Your soul is ill. You think you are equal to God. Cast out your demons, sir; do it soon, before it is too late.

>> No.12764506

>>12764203
>Nope, it is an addition
Nope, it's a union of the indicator function for clay.
Addition is the combined measure when two measured amounts of clay are put together.
Your clay function simply indicates that an unmeasured amount of clay exists when one or more unmeasured amounts of clay are put together.

>> No.12764913

>>12764323
Stop lecturing me and stop being an hypocrite.
The ones who virtue signal most lack the most their virtues.
You know I am right, deep down, and that is why you are full of fear when confronting me. You lack faith. You believe in a lie.
Nothing in this material world is eternal. Only the spiritual is.

>>12764506
It is no union, but an addition.
The meaning behind 1+1=1 is what matters, not the symbols used.
Add two lumps of clay together and you get one lump of clay. Putting them together is exactly the same as adding them together.

>> No.12764978

>>12764913
>Putting them together is exactly the same as adding them together.
No, there is a devil in your semantic games.
>>12763846
>You have yet to tell me a single thing that has neither beginning nor end.
I have found something with no beginning and no end.
It is your arrogance.
Yes, your arrogance is infinite.

English is not even your native language (I hope), yet you would stand and speak with deific authority on the meaning of English words you don't even understand.
You have the eyes of a man, yet you would stand and speak as if you had the eye of God.
You have the creeping fear of a man, yet you would stand and speak as if the world itself were fearful of your trembling shadow.

Your only salvation is humility. The choice is yours, but like all men, you have a choice.
You have a choice.

>> No.12765082

>>12764913
>>12764913
>The meaning behind 1+1=1 is what matters
The meaning of addition is that you combine two measurements. If there is no measurement, there is no addition.

In English, "clump" is a word specifically used to mark the noun it modifies as unmeasured, or unmeasurable. If you simply write "add 1 clay plus 1 clay," without using the weasel word clump, there is no ambiguity that you have 2 clays. If you unmeasure the clay by saying "mix 1 clump of clay into 1 clump of clay," it has a completely different meaning which has nothing to do with addition.

>> No.12766530

>>12764978
False. Stop being an hypocrite. Stop blaspheming by seeing nothing but evil in others.
I have never seen such self-righteousness coming from anyone.
The search for immortality is something that has to do most with devil worshippers.
Everything has a beginning and an end in this world.
One day you will regret lecturing me. May you forgive yourself once the time comes.

>>12765082
Add two separate units of clay and you get exactly and without ambiguity one unit of clay. Simple. No need to get your brain all messed up over it.
1+1=1
Math is a language. Nothing more. It is a tool for communication, not truth.

>> No.12766668

itt: idiot incapable of learning elementary math invents Coelho-level bullshit in a bid to pretend to have something worthwhile to say.
noticeably missing: an acknowledgement that in the classical conventions 0.999... indeed equals 1. this is because aforementioned moron has no idea what the standard conventions are.

>> No.12766688

>>12766668
0.999... < 0.TTT... < 1

>> No.12767068

>>12766530
>I have never seen such self-righteousness coming from anyone.
All you need to do is look in a mirror.

>>12766530
>Add two separate units of clay and you get exactly and without ambiguity one unit of clay.
False. Your arrogance blinds you and makes you speak with a forked tongue.

>> No.12767086

>>12766688
False. 0.999... = 0.TTT... = 1

>> No.12767195

>>12767086
Nope, see here >>12758057

>> No.12767242

>>12767195
lim n->∞ (2^n-1)/(20^n) = 0

>> No.12767276

>>12767195
there's an obvious flaw

>> No.12767401

>>12758057
I was impress that even if everything you were doing was unusual, it was correct.
And then I got to the last line, [math]\lim_{n\to \infty} \frac{2^n - 1}{20^n} > 0[/math].
That limit is 0. What do you think [math]\lim_{n\to \infty} \frac{2^n}{20^n} > 0[/math] is?

>> No.12767460

>>12767401
>>12767276
>>12767242
It's simple any positive number you can think of > 0+ > 0 > 0- > any negative number you can think of.
lim n->infinity 1/n = 0+
lim n->-infinity 1/n = 0-
The only problem is that modern mathematicians lack rigor, so they do shortcuts like 0 = 0+ = 0- when in fact 0 is neither a positive nor a negative number, unlike 0+ and 0-.

>> No.12767470

>>12767460
>any positive number you can think of > 0+ > 0
is 0+/2 lesser or greater than 0+ ?

>> No.12767488

>>12767470
Is infinity / 2 < infinity?
undefined.

>> No.12767491

>>12767488
>Is infinity / 2 < infinity?
no. inf/2 = inf which is not lesser than inf

>> No.12767554

>>12767491
There is no way to tell if inf/2 = inf, so it remains undefined. You would have to check if every digit of an infinite number equals every digit of another infinite number. Impossible.

>> No.12767557

>>12767554
inf = inf/2 by definition.

>> No.12767560

>>12767401
From what I gather, he wants to assign a composite expression 0+ to that limit, because the terms of (2^n-1)/(20^n) approach the limit of (2^n-1)/(20^n) monotonically from above. It's a perfectly valid concept, in that 0+ does indeed express an additional information not contained in the number 0 itself. What he doesn't seem to understand is that the composite expression 0+ isn't a number, it's a number composed with an additional piece of information, which in this case is a signed indicator of whether some sequence of numbers with a limit approaches that limit monotonically.

>> No.12767566

>>12767554
inf/2 = inf, simple as

>> No.12767581

>>12767460
see>>12767560
0+ isn't a number, it's a number combined with an additional non-number piece of information.

>> No.12767588

>>12757950
A sandstone is 1, but contains millions of grains. So the sandstone is 20 million? No, it is unified, it is 1.

>> No.12767598

>>12767588
If a sandstone contains 20MM grains, and you have 1 sandstone, then the number of sandstones you have is 1 and the number of grains you have is 20MM.

>> No.12767604

>>12767560
>>12767581
This. We can formally define

[eqn] a^\pm := a \pm \lim_{x\to\infty} \frac{1}{x} [/eqn]

for any real number [math] |a| < \infty [/math]. It's useful to define as it tells us whether you've constructed a least upper bound or a maximum lower bound. However, algebraically,

[eqn] a^\pm \equiv a \qquad \forall a < \infty \in \mathbb{R} [/eqn]

>> No.12767625

>>12767604
>We can formally define
>a±:=a±limx∞1x
then a± = a, because the limit is provably 0

>> No.12767628

>>12767625
Ugh, yes? that's literally the second of two equations in my comment bro. Are you high? I'm merely quantifying the claim that this [math]a^\pm[/math] carries extra information, namely tracking upper bounds or lower bounds

>> No.12767670

>>12767581
0+ is the lowest positive number you can think of.

>> No.12767682

>>12767628
>>12767628
you're not saying anything
[eqn]a^+ = a \\
a^- = a\\
a^+ = a^-[/eqn]

>> No.12767688

>>12767682
Do you not understand the difference between least upper bounds and maximum lower bounds?

>> No.12767692

>>12767688
I do. but [math]a^{\pm} = a \pm \lim_{x\to\infty}\frac{1}{x}[/math] has nothing to do with it. it doesn't say anything else than [math]a^{\pm} = a[/math].

>> No.12767718

>>12767598
Reverting to the clay function.
When two clays are clumped into one clay, we get the operation

[math]1\oplus1=1[/math]

Curiously, we can also describe an inverse clay function, whereby one clay is declumped into two clays.

[math]1\ominus1=2[/math].

What would be the best formalization of this declumping operator?

>> No.12767727

>>12767718
>What would be the best formalization of this declumping operator?
you can start with arity. it's obviously an unary operation, not binary.

>> No.12767748

>>12767670
Then it's not 0. You're describing the reciprocal of "MOAN."

>> No.12767755

>>12767727
>not binary
But we can declump 2 clays from 1 clay, giving us 3 clays: [math]1\ominus2=3[/math]

>> No.12767783

>>12767755
Never mind, declumping is just subtraction written backward lol. What a huge bore.
[math]1\ominus1=2\;\Leftrightarrow\;2-1=1[/math]
[math]1\ominus2=3\;\Leftrightarrow\;3-2=1[/math]
[math]3\ominus5=8\;\Leftrightarrow\;8-5=3[/math]

>> No.12767808

>>12767783
i.e, addition. so in terms of clay, when you declump x clays from y clays, you get x+y clays

>> No.12767961

>>12767460
You're thinking of this
https://en.wikipedia.org/wiki/Arithmetic_underflow
The signed zero doesn't exist in R because there's no underflow in calculus.

>> No.12768053

>>12767748
It is 0+, the positive version of 0.
0- is the negative version of 0.

>> No.12768072

>>12757950
this is why math is fake

>> No.12768163

>>12768053
0 is the additive identity, it can't be positive or negative.

You're trying to establish an underflow value in a number system that is defined by infinitesimal calculus rather than discrete calculus. Underflow is incompatible with that design.