/lit/ - Literature

>>17393773
Well an infinity of both odd and even numbers is twice as large as an infinity of only odd numbers, for example.

>>17393773
This machine kills facists.

>>17393773
This seemingly banal and particular truth is somehow way more infinitely important than your banal and particular truth, but they are all equal unless those infinity dont quite fit into my own.

>>17393773
exactly what he was saying
unfortunately modern maths is based on your infinite recursion bullshit so he will eventually be proved wrong

>>17393773
This Fascist kills machines. (pbuh)

>>17393791
No it isnt retard. Look up cantor's diagonal argument

>>17393773
Ignore it, it's just some meme in the math community that was originally said by some Jewish schizo. The sad thing is, pseuds like this midwit actually believe it and uncritically repeat it like it means anything.

>>17393773
Dunno, anon. It is like >>17393791 said. Some infinite sets are able to contain other infinite sets. https://en.wikipedia.org/wiki/Aleph_number

>>17393811
You are very rude and I don't care for you.

>>17393815
> MUH THEOREMS, YOU CAN"T COMPARE INFINITITIES, NOT A NUMBRE. CAN'T CONCEIVE ANYTHING MEANINGFUL OUT OF IT.

And he got it mixed up too. Uncountable infinity is infinitely larger than any countable infinity. Green thinks the all of the numbers between 0 and 1 is a smaller infinity than all real integers. What a moron

>>17393791
False. They both have the same infinity, which can easily be proven in mathematics.

>>17393773
>What did he mean by this?
Real numbers are bigger than Natural numbers, that is, some infinities are bigger than other.

>>17393832
yes

>>17393840
But it is kinda stupid anyway. More like the kind of thing that regular people would call mathematical autism.

Isn't this a mathematical question? Did he get this idea from an actual mathematician? Also what the fuck is that supposed to philosophically imply?

>>17393870
> Also what the fuck is that supposed to philosophically imply?

Maybe some stuff about infinities. Probably just more stuff to people play with.

>>17393773
my cock is infinitely bigger than yours

>>17393918
so it's essentially wank

>>17393920
Most of math starts as such, anon. Check the Greeks out.

>>17393840
>countable infinity

>>17393936
This is probably any set of things that can be 'linked' 1-to-1 to the natural number set.

https://en.wikipedia.org/wiki/Georg_Cantor That aleph stuff is probably too weird for /lit/ but this is the mathematician who invented that.

>>17393773
There are infinite values between 0 and 1 (0.1, 0.01, 0.001...), and twice as many infinite values between 0 and 2, because the distance between 0 and 2 is twice as big as the distance between 0 and 1.

Well its like this
If one infinity got a head start it will spread farther into infinity.

>>17393936
Are you retarded? If I start with 0, I can count 1 2 3 4 all the way up to infinity in an infinite amount of time. That is a countable infinity. Take the amount of numbers between 0 and 1. Start at 0, what number is next? It is impossible to even count the numbers in between 0 and 1, making it an uncountable infinity. Countably infinite is a term mathematicians use

>>17393857
That is what got me into Physics. KEK

>>17393773
that is literally a true statement

>>17393791
13579
12345

For example natural vs real numbers.

>>17394000
No, bijection (assigning each number from second interval unique number from first) is trivial.

>>17393773
To put it a bit informally, if a bijection does not exist between two infinities then they are not equivalent. In other words if each member of one set cannot be mapped to one and only one member of another set then one set is greater than the other. There is no bijection between the natural numbers and the real numbers.
>>17394000
The set of real numbers between 0 and 1 has the same cardinality as the set of the real numbers.
You people need to brush up on set theory.

>>17393791
Lol

>>17393791
Based as fuck

what if there is one infinitely long penis with 10cm girth. and another infinite penis with 20cm girth. the latter is bigger infinity. qed

>>17393773
>>17393791
>>17393811
>>17393816
>>17393832
>>17393840
>>17393843
>>17393866
>>17393870
>>17393918
>>17393920
>>17393959
>>17394018
>>17394213
>>17394284
>>17394404
Full section:

"There are infinite numbers between 0 and 1. There's .1 and .12 and .112 and an infinite collection of others. Of course, there is a bigger infinite set of numbers between 0 and 2, or between 0 and a million. Some infinities are bigger than other infinities. A writer we used to like taught us that. There are days, many of them, when I resent the size of my unbounded set. I want more numbers than I'm likely to get, and God, I want more numbers for Augustus Waters than he got. But, Gus, my love, I cannot tell you how thankful I am for our little infinity. I wouldn't trade it for the world. You gave me a forever within the numbered days, and I'm grateful."

>>17393773
>What did he mean by this?
well probably the same thing as what georg cantor meant

Joh green: the genius, throwing shade at Shakespeare

"But it is the nature of stars to cross, and never was Shakespeare more wrong than when he has Cassius note, ‘The fault, dear Brutus, is not in our stars / But in ourselves."

>>17395357
This is 100x worse than when David Foster Wallace attempted math.

>>17393773
The cardinality of the real numbers is larger than the cardinality of the integers, for example.

>>17395357
>There are infinite numbers between 0 and 1. There's .1 and .12 and .112 and an infinite collection of others. Of course, there is a bigger infinite set of numbers between 0 and 2,
I think some people should avoid math, they are too dumb for that.

>>17393773
|N| < |R|
or equivalently
∄f: N R such that f is surjective

Scientism

>>17395377
I knew bugmen were incapable of taking responsibility for their actions but I didn't know they admitted it so openly

>>17395357
>>17393773
I read somewhere that John Green deliberately got it wrong because he didn't want his characters to always be right.

>>17395975
I read somewhere that John Green sucked a guy off behind Wendy's.

>>17393773
hasn't anybody done basic fucking calculus around here?
when calculating limits you literally come across infinities that are smaller so they can be ignored when considering a bigger one.

ok

>>17393811
This. Odd and evens, even when added together or split, are still the same size of set. It's reals vs integers where you end up with different sizes of infinity (based precisely on cantor's diagonal argument)

>>17393773
It's like when kids argue by saying they're right times infinity and the other kid says oh yeah well I'm right times infinity plus one.

>>17395377
Did he actually write this? Holy shit, what a hack.

>>17396337
No matter how many irrationals you have to count, you will always have an integer available to count it with. Always. Therefore, the claim that there are more irrationals or reals than integers or rationals is nonsense.

>>17393773
He was talking about infinity tattoos

Infinity/1 is greater than 1/Infinity

>>17396015

>>17398586
>it's real

>>17396127
I think you are retarded, anon. You don't calculate smaller or bigger infinites, when taking the limit, in some cases, some functions tend to approach infinite faster than other, which helps when taking the limit. It has nothing to do with a bigger or smaller infinite.
Given that you took calculus, you should know about Cantor and how the reals has a bigger infinite than the natural(which has the same infinite as integers and fractions).
t. a mathematician

>>17396423
Cantor is wrong and this anon is right.

>>17396423
Inaccessible cardinals go brrrr

>>17396423
Bait

>>17393773
There's not "bigger or smaller" there's "countable or uncountable"

That's it

>>17398777
there are higher alephs, my man

>>17399146
While in some sense cardinality is like an abstract way to understand the size of a set, outside of a mathematical context it's an abuse of language to talk about a set's cardinality as its size, because we intuitively associate size with physical properties like width, length, extension, etc.

>take the biggest infinity you can think of
>add 1 to it
>always get a bigger infinity than the older infinity

>>17398777
Yeah "big" is a stupidly imprecise term
>Grug think this infinity small, but grug think of bigger infinity. Small infinity is not as big. Grug like big infinity

>>17399217
sure bigger and smaller are an abuse, but it's not just countable and uncountable either.

>>17399259
Agreed mate, not really sure why I chose your comment to respond to.

Its more accurate to say that some infinities are more dense than others

>ITT, litfags fail at highschool math

>>17399229
Infinity is not a number anon, you cannot add to it

>>17393857
I made this picture

Infinity is a transcendent concept which is outside of all possible experience, ergo it is worthless attempting synthetic judgements with it (ie mathematical judgements). Mathniggers BTFO by this one little Prussian

>>17400217
But that's wrong

>>17400253
Show me infinity then.

some infinities are larger because of time. possibility may be endless but growth is measurable. if we measure separate infinities at distinct times some may be larger because their rate of growth is more. also some may have begun at earlier times.

>>17400254
Do you believe the set of natural numbers exists? Or is it that you believe the set of natural numbers exists but there is a largest natural number?

>>17400397
>Do you believe the set of natural numbers exists?
Yes, but only conceptually. The set of natural numbers is itself transcendent, even though it rests on a reasonable formulation. Synthetically reasoning with the set of natural numbers is pointless (is the set of natural numbers greater than the set of rational numbers?), analytically reasoning with it is fine (do prime numbers exist within the set of natural numbers?, etc.)

>>17400445
This is so confused. So the set of natural numbers is conceptual but natural numbers have some real existence? And if you think natural numbers are purely conceptual instead how can any synthetic reasoning about them be meaningful and how does that cohere with Kant's idea that all math is synthetic? And how is the existence of primes analytic instead of synthetic?

>>17393773
SOME INFINTES ARE BIGGER THAN OTHERS
SOME INFINTES ARE BIGGER THAN OTHERS
SOME INFINTES ARE BIGGER THAN
OTHER INFINTES MOTHERS

>>17400500
>So the set of natural numbers is conceptual but natural numbers have some real existence?
Yes, I don't see what's confusing about this
>how does that cohere with Kant's idea that all math is synthetic?
He was speaking of mathematical discovery. Mathematical discovery isn't made by analyzing things we already know.
> And how is the existence of primes analytic instead of synthetic?
Well, if one were trying to show that any given number were a prime or not (because its primacy is indeterminate), that would be a synthetic judgement. But using the pre-established idea of a prime when analyzing the natural numbers only yields a result that is already within the concept of the natural numbers, which is to say we only analyzed the concept that already existed, we didn't add anything to our concept.

>>17400500
Actually, hang on, I understand your confusion. I fucked up using the discovery of primes within the natural numbers as an example of analytic. A correct example would be "does the number x, which is a natural number, exist within the set of natural numbers", which is a truism. I think the problem arises only when dealing with the concept of infinity synthetically, rather than any given set. (which might have an infinite magnitude, but is not the entire concept).

>>17400549
The idea of a set is a lot more intuitive than a number. Set theory is the logical basis of modern math.

And as for a specific number being prime how could that possibly be indeterminate? You may not know if it is but the fact of it being prime or not is definitely in the concept of the natural numbers. How about the existence of an odd perfect number? That asks about number theoretic properties just like primality. Do you think that is somehow analytic when we don't know the answer and a proof of the existence(or non-existence) an odd perfect number would be lauded as a legit mathematical discovery?

>>17393773
Are you telling me that some infinities are more stretched out than others? Well screw you, infinities. Just because your black holes are looser does not mean I can't still enjoy your whole gravity crunch.

it show the gross misuse of infinite in mathematics

>>17401341
It's not misused, you just don't understand it

>>17401372
I've read the proofs, I understand it just fine. But you cannot proof two things which contradict their definitions.

>>17401417
???

>>17401417
There is no bijection from the natural numbers to the reals. All of those terms have specific formal definitions in math and if you've discovered a contradiction in Cantor's proof with them you're going to be famous

>>17401417
If you're so smart, why aren't you rich?

what is a natural number?

>>17401800
a morphism from the final object of a category to the object satisfying the universal property that for every object A and morphisms q and f as pictured there is a unique u such that pic related commutes

>>17401494
let me spell it out for you. either the definition of 'infinite' is incorrect or(and) the operation where you list infinite series of numerals is incorrect or the operation where you add to this list is incorrect. no must give away for the definitions to be true.

>>17401513
based Dick Head

>>17393791
Retarded mathlet

>>17401948
The real way everything works uses functions with nice finite definitions. Here's the way I think you can resolve all of the issues you brought up:

"infinite" isn't usually the word used during the proof, since it's a bit overloaded. But the definition of infinite is usually "there exists a proper injection from X to X." To prove this is true, you don't need to list all the elements of X, you just need to define a function on X.

The operation of "listing the elements of X" isn't really "creating an infinite list, all at once" - it's really "creating a function from N to X." A function is just a rule - you take one element of N, you get an element of X back. Rules are nice and finite; no problem with infinities there.

Adding to the list: you're saying an element y isn't "in the list" - but since it's not exactly a list, it's a map, you're really saying "there is no n in N such that n maps to y." Nice, finite proof: assume such an n exists, derive a contradiction.

The other part of "adding to the list" that might seem problematic: the construction of the element itself, which does have a tricky infinite part. But that can be resolved with functions as well.
Constructing a real number as a series of digits , like 3.14159.... is, like with the earlier "list," actually the creation of a map N -> D, where D is the set of digits 0 to 9. The rule for the element we create in the diagonal proof is (pretty much) "n maps to the nth digit of the nth element of the list of real numbers, plus one." But that definition doesn't have to deal with anything infinite: once you pick an "n," you only need to think about the first n elements of the list of reals, and the first n digits of those real numbers. So it's a well-defined function without having to deal with a whole infinity of things all at once.

>>17395702
The quote is about kids getting cancer lol

>>17393773
isnt this what joe rogan was talking about in those youtube ads?

>>17402673
Their own fault as well

>>17402673
You think cancer just happens? The shit air we breathe and the shit lab created food we put into our bodies catches up eventually. I'm not saying it's the kids fault he got cancer but hunter gatherers didn't have to worry about bullshit like that

>>17403258
fun fact: elephants are highly resistant to cancer due to several duplicated genes

>>17403258
I don't disagree about the air and processed food not being great, but how exactly would we find out how much cancer the hunter gatherers got lmao

>thread about an album
>thread about how to get a shy gf
>thread about math
>thread about posting anime girls
Jannies really do work hard for their pay

>>17402673
nigger kids deserve cancer

That time is relative.

>>17394018
> Start at 0, what number is next?

Pic related. Nothin personnell kid

>>17396015
And that guy was Albert Einstein

>>17393773
I just have to say it.
john green molested me a few years ago. I hate seeing him on the board. I'm a male btw.

>>17405111
Yes, true. And this guy also molested me.

<<<<

He was a pedophile and lured me to his home with candy where he whipped his chode out and started jizzing all over the place.

>>17405118
It's not a fucking lie.

>>17393773
Set theory is like 5th grade math, anon

The infinite amount of numbers between 1 and 3 is double the infinite amount of numbers between 1 to 2

>>17403269
god I hope I get to be an elephant when I reincarnate, they seem so based

>>17405003
Not nice anon

>>17400205
Proud of you anon!

>>17393791
why dont you prove it, smart guy

he meant that there exists a mapping between the countably infinite space and the uncountably infinite space, and such a mapping is necessarily onto.

Men and women are equal but women are superior.

>>17406631
go away reals >:(

what is all this math bullshit hitler was right!

How does /lit/ feel about the Riemann Hypothesis?