/sci/ - Science & Math

>>10203514
A lot

>>10203514
2^(2^64)
2^(2^64)+1 breaks the universe; don't type it into a calculator because it will literally segfault the universe

>>10203536
my computer saw that number and crashed wtf how do i fx it?

>>10203562
it's done for. the only fix is to replace the motherboard.

>>10203514
get the fuck off this board you disgusting plague vector

>>10203535
At least a lot.

>>10203514
Something like (average number of states of an elementary particle) to the power of (number of elementary particles). More realistically, you would only account for the information that can plausibly be changed in our future light cone.

The precise number will probably remain unknown for all times, but Landauer's principle can give us perhaps an upper bound.

>>10203603
>finitist subhuman
>>10203663
+1

>>10203663
There are infinite elementary particles.

>>10203678
We don't know that. Due to the expanding universe the accessible/visible part will possibly always remain finite even though the entire universe might be infinite.

>>10203663
>>10203678
>>10203688
The universe is utterly irrelevant

>>10203668
No i mean groyper posters

>>10203696
Whoops my mistake, sorry anon

>>10203688
It's the simplest explanation, Occam's Razor.

>>10203730
guideline, not a rule dumbass

>>10203514
An unbounded number

>>10203663
Shit argument.

You can take this number you claim is the biggest and subtract 1 particle.

Now use this particle to represent the almost "biggest" number. Now you can start counting again, adding to the placeholder. In this way, you can recursively define any number.

this is like asking for the solutuion to a = a + 1

>>10203753
But then you could not count from 1 up to that number, could you? It is impossible to add more information without bringing another elementary particle into existence.

>>10203663
is that number plus 1 not an integer then???

>>10203514
Finitists accept an infinite set of integers. Ultrafinitists do not.

>>10203739
>We don't know that leprechauns aren't causing global warming
>>We do, Occam's Razor
>It's just a guideline not a rule dumbass

Technically, the number of numbers can be finite. The limit is the capacity of whatever is currently counting toward infinity and retain a solid structural state, whether physically or in sub-molecular space. Humans have a limit, calculators have a limit, computers have a limit, and even general objective space has a limit depending on the media.

Finite by rule of its container*

>>10203885
that + 1

Infinity exists in finitist models, it's just a large cardinal

>>10203663
>the absolute state of finitist retards

>>10203753

No your argument is shit. When we talk about particles like this we are literally saying there is a glass representing the the informational capacity of the universe as we currently conceive of it, and it is full to the absolute max, that absolute max of elementary particles, and their states is the limit. You can't 'start counting again' at the limit of physical capacity just because you created one open slot.

Induction doesn't exist, and recursive definitons aren't numbers.

>>10203955

What is doing the calculation to add the plus one? That thing doing the further +1 you reference also has a discrete limit, whatever mechanism is doing the 'counting' if negative entropy exists, has a limiting factor on that mechanism.

>>10204023
You really don't understand math.
I don't need to be able to calculate something for it to exist. For example, I can talk about the number of possible configurations of all the particles in the universe without being able to write it down in the same way I can talk about the number of trees on earth without knowing exactly how many there are. Likewise, I can talk about a number equal to 2 times the number of trees on the earth without actually writing out the number of trees and multiplying it by 2 à la elementary school. Math is all about abstractions, and you seem to be missing some crucial abstraction level in your thought. If you've ever read about developmental stages of learning you'll know that humans move through object permanence, through egocentrism, through rational thinking, and while developmental psychologists usually stop there there are certainly differing levels of cognitive abstraction that people pass through in their cognitive development past the first checkmark of logical thinking.
You might want to look up googolism. I think it might broaden your horizons a little.

>>10203880
Nice semantics you got there, buddy. People might have gotten confused. Anyway, sorry for misgendering you.

>I don't need to be able to calculate something for it to exist.

>>10203514
Integers don't exist. Have you ever seen integer for example in Forrest? It's just concept. And you can conceptualise almost anything. QED you are stupid frogposter.

>>10203514
That's a non-question
Not every question has an answer..
Infinity still doesn't exist

>>10204019
I understand the argument.
Please tell me why each particle can only represent 1 number instead of 2 or 50 or the max number.

Numbers don't exist physically, they are an abstraction that can be defined arbitrarily.

finitists are literal subhumans

>>10203514
The question has no answer as you can create any integers.

>>10203514
infinity - 1 to be exact

>>10204181
braindead

>>10204181
>tsp for one million cities, a shortest path exists but we cant fucking calculate it
>cant calculate any irrational number
>cant calculate every zero for the Zeta function
>calculations depend on the computer you're using, so now numbers are subjective
>"my computer says that sqrt(2) = 1.4, mine says sqrt(2) = 1.414
>"my computers overflow limit is 64, so 65 doesnt exist"
kill yourself

>>10203514
it completes everything

>>10203514
>>10203514
>There are only so many particles in the universe, so infinity isn't real.
Implying there are a known number of particles in the universe
Implying particles can only hold a finite number of states
Implying there are a finite number of different types of particles
Implying space is quantized
Implying space is finite
Implying time is quantized
Implying time is finite
Implying there is nothing outside of the observable universe
Implying there is nothing outside of materialism (ie consciousness doesn't exist)
Implying there is a real thing called a "particle"
Implying all abstractions have to be instantiated in the material world to be relevant
Implying there is a real thing called a "number" in the existence
Implying the mathematical concept of a limit is invalid despite all understanding of the material world being based on it

>>10204371

The question was not "what is the largest integer", but "how many are there". The number of things we can refer, where things is most broadly defined as configurations of the universe, to is limited by (number of states)^(number of particles). It is of course smaller because if we use up the particles of our brains to represent a particular thing, then we cannot think about it anymore.

>>10204781
>the number of things we can refer to...
the number of states per particle to the power of the number of particles
...PLUS ONE!
haha feels bad to be proven wrong so instantly doesn't it lmao.

Esenin-Volpin already BTFO'd all the brainlets asking this pseudoquestion:

>>I have seen some ultrafinitists go so far as to challenge the existence of 2100 as a natural number, in the sense of there being a series of “points” of that length. There is the obvious “draw the line” objection, asking where in 2^1, 2^2, 2^3, … , 2^100 do we stop having “Platonistic reality”? Here this … is totally innocent, in that it can be easily be replaced by 100 items (names) separated by commas. I raised just this objection with the (extreme) ultrafinitist Yessenin-Volpin during a lecture of his. He asked me to be more specific. I then proceeded to start with 2^1 and asked him whether this is “real” or something to that effect. He virtually immediately said yes. Then I asked about 2^2, and he again said yes, but with a perceptible delay. Then 2^3, and yes, but with more delay. This continued for a couple of more times, till it was obvious how he was handling this objection. Sure, he was prepared to always answer yes, but he was going to take 2^100 times as long to answer yes to 2^100 then he would to answering 2^1. There is no way that I could get very far with this.

>how many integers are there?
the largest integer you can enumerate fully. It is limited by the ways you can order particles in the universe. You might be able to describe a larger number using a fancy notation, but you won't be able to enumerate the integer fully.

>>10205094
(the largest integer you can enumerate fully) + 1
lmao btfo yet again

>>10205094
low iq post

the universe is finite but uncomputable

>>10205094
but after ordering all the particles in the universe, then you yourself would get rearranged and so you couldnt confirm that.
therefore there doesnt exist a largest integer, finitism is stupid, just use modular arithmetic if you care that much

>>10205725
the last panel is brainlet

>>10203872
where are you getting that 1 from, retard?

>>10205764
the whole thing is a strawman with agnostic in reality being the technical only real logical solution even though i'm a theist

>>10205056
Plus one does not make sense because it cannot exist. The axiom system is not closed under addition, easy as that.

>>10205801
Imagine being this big a brainlet holy shit

>>10205080
Esenin-Volpin is the brainlet who thinks 2^100 isn't a number did you read this fully?

>>10203536
>>10203663
>this is your mind on finitism
Absolutely retarded

>>10203514
integers are a concept of the human brain, they're infinite if we want them to be

>>10205775
my brain, I guess. You need some? I have a few left over

>>10204501
so... there are infinitely many

>>10203514
The problem finitists (and really most non-Platonists) have with these concepts is that once you realize the Truth of the matter, you are forced into accepting the Infinite Platonic Ideal Realm and these scienshits and engicucks refuse to accept the existence of a more fundamental and infinite non-empirical reality that is a superset of this finite universe and it's finite list of laws of physics.
This is why they'll say things like "gO bAcK tO /x/" whenever you bring these things up. Their small brains literally can't conceive of non-empirical truths. Like animals writhing in the filth, they can only think of things their sensory experiences have stimulated.

>>10205995
Yes, I did read it. Any arguments for why 2^100 is a number, buddy?

>>10206983
flip a coin 100 times

>>10206991
Fair enough. Another acceptable answer would have been to just compute it---2^100 is still feasibly computable, but as was said in the story (did _you_ read it fully?):
>There is no way that I could get very far with this.
Try 2^(2^100).

>>10203514
There are arbitrarily many, you just can't prove that the integers are a set.

Any answer to this question that isn't this is a pseud answer.

Let us analyze the amount of possible moves in a standard game of Go on a 19x19 board with the rules and the rule of KO.
The set of all possible boards is absolutely enormous, many times larger than the amount of particles that exist in the universe. And yet, they are still finite, and can be completely actualized on the board. The number can be given an upper and lower bound, and computation can be performed on it in finite time (although, the length of time would surpass the length of the universes lifetime).
What finitists are asserting, is that these possible board states of Go do not exist, because they can't be computed in this universe. That is utter nonsense. The board states objectively exist even if we can not get to them in our universe.
Now take the set of all true statements that are unprovable under a consistent but finite list of axioms. The number of such statements is INFINITE. Within that list, all possible states of the board of Go, all possible states of the universe, of the permutations of a deck of cards, of any proposition in math, all exist. Even a statement like “All even numbers greater than 4 are the sum of two primes" (Goldbach’s conjecture) may not be provable under our current finite set of axioms, and yet whether or not this statement is true DOES EXIST even if we can not yet prove it. The statement doesn't "become" true or "become" false when it's proven as such - whether or not it’s true objectively exists, and we find it (which may or may not only be possible under some other set of axioms than the ones we currently use).
The finite list of provable statements we have under the current finite list of axioms are a subset of the infinite list of the ideal realm. The finite list of the laws of physics of this universe, and of all possible states of this material universe are a finite subset of the infinite list of the ideal realm.
This “Material Universe” is not fundamental.

Let M be the largest number.

M

/sci/ can we kill all the platonists yet?
they try to ruin every thread they touch

>>10203514
>If infinity doesn't exist, then what is the integer number between 3 and 4?
How to even compute the number of numbers? What if the number of numbers doesn't exist, how is it related to existence of anything?

>>10207001
under what set axioms?
with naive set theory you can just say "the set of all integers" and BAM its a set. In ZFC you can have a set of integers as well, although I won't post the proof here.

>>10207057
Let M be henceforth referred to as "infinity"

>>10207464
wut
the absolute quantity of wut

>>10207796
nope, infinity isn't a number

>>10207837
oh so you claim that M doesn't have all the properties of infinity?
Because M also isn't an integer (suppose M is in Z. Then for all x M>x. but M+1>M, so M is not in Z)
M also is additively absorbtive (M+1 = M because it can't be larger than M)
and larger than any integer (your definition)

>>10207861
https://www.wolframalpha.com/input/?i=infinity
An unbounded quantity that is greater than every real number.

you tell me
how is a number "greater than every real number" ?
I'll wait

Ok, who keeps bumping this thread? I saw this post about two days ago, and it hasn't been scrapped.

Back to the question: Impossible to tell

>>10207100
still no argument against it
you know platonism is right anon, accept it

>>10207003
There's a mistake here.
The infinite Ideal Realm is not a list (it's uncountable) and thus this line
>finite subset of the infinite list of the ideal realm.
doesn't work, it asserts the ideal realm is isomorphic to the naturals when it's isomorphic to the reals.

>>10207884
you said it yourself in your definition

>>10203514
There are only two integers, 1 and -1, the rest is the work of some autist

>>10203514
How does an integer exist if it can’t model reality or be conceived in some way?

>>10208393
This universe/material reality does not constitute all of reality.
it is a finite subset

>>10203514

arbitrarily many.

give me (i.e., CONSTRUCT) any cardinal number and I'll show you a proof that there are that many integers.

We have actually already proven it for all of them at the same time using universal quantification

>>10208802
the cardinality of the reals.

>>10203514
Let N be the number of integers. It's easy to show that N doesn't exist. If N=∞, then ∞ doesn't exist because N doesn't exist, kek.

>>10208381
LOLno
lrn2read

>>10203514
uncountable.

Infinity conveniently adopts and hijacks uncountability, but uncountability is a seperate concept.

it benefits neither finitism or infinitism to consider how many integers there are. Your brain is pudding.

>>10208832
>cardZ is the definition of countable
>cantor found cardR is strictly greater and it got called an uncountable
How in the name of fuck can cardZ possibly be uncountable

>>10207003
[math]3^{19^{2}}[/math] accounts for every possible configuration of the board.

this is not relevant to making a GO-playing AI though.

>>10208830
>>10207057
>Let M be the largest number
if that's not what you meant then lrn2speek

>>10208802
>give me (i.e., CONSTRUCT) any cardinal number and I'll show you a proof that there are that many integers.
1

>>10209230
stop assuming those two are the same person

>>10207057 is bs, ignore it

>>10203514
In a universe that contains a finite amount of things in it at a given timepoint it would not be possible to count above that amount without altering said universe in said timepoint.

Infinity is more of a practical physics question

>>10209769
universe has 10^80 particles
so obviously no one could figure up a googol

>>10209769
Again, see >>10207003
mathematics is in no way restricted by or contingent on this universe
Quite the opposite, this universe is contingent on the infinite mathematical ideal realm

>>10204133
Could have just shortened it to math is made up bullshit.

>>10209946
>t. brainlet


I'm just going to say it clearly: if you genuinely can't understand the things being said about how math is discovered and the universe is not fundamental, YOU. ARE. NOT. SMART

>>10203514
Where does this meme come from? I mean the OP image

>>10209952
1/3 = 3.33...
3*3.33... = 9.99...

Checkmate mathtard.

>>10209971
I dont even understand what it is you're attempting to say with this.
unless you're one of those "9.99999... =/= 10" retards lol

>>10209971
>1/3 = 3.33...

>>10209980
>unless you're one of those "9.99999... =/= 10" retards lol

I dont see any counterargument. Only namecalling.

>>10210020
the counterargument was given over a hundred years ago

>>10204181
Literally true, retard. How big do you think the brain is?

>>10204781
Number of particles is not a fixed quantity you mongoloid middle-schooler.

>>10210024
>This shit makes no sense.
>Just make up more bullshit until nobody cares anymore.

Just accept that all math is arbitrary and made up before you embarass yourself further.

>>10206995
Number of sets of coin flips.

>>10210020
1/3 = 3/10 + 1/30
= 0.3 + 1/30
= 0.33 + 1/300
= 0.333 + 1/3000
:
= 0.3... + 1/inf = 0.3... + 0
= 0.3...

>>10210059
It makes perfect sense and if you can't understand it, that is a limit of your own capabilities and not of the system or the results that you are taking issue with.
Math is not arbitrary nor is it made up. There is no embarrassment in my position, which the position of the vast majority of mathematicians as well as just humans in general.

>>10207837
https://en.wikipedia.org/wiki/Extended_real_number_line
https://en.wikipedia.org/wiki/Real_projective_line

>>10203514
No one has given the correct answer yet. Disappointed in /sci/.

The answer is aleph zero, the first transfinite cardinal, which by the von Neumann cardinal assignment is equal to omega, the first transfinite ordinal, which itself is equal to the union of all finite ordinals.

>>10210068
>divide by infinity
>0.33... = 0.3
>0.3*3 = / = 1

At least we can agree that this shit makes no sense.

>>10210112
each line in >>10210068
equals 1/3

it is your job to prove that the value drifts away from 1/3
protip: it doesn't

https://www.wolframalpha.com/input/?i=1%2Finf

>>10210141
So the solution is 1/3 = 0.33... = 0.3*3 = 1 ? No wonder no one takes mathematicians seriously.

>>10210162
>t. brainlet

>>10210172
Not an argument.

>>10210162
not a bait, not funny
just sad

>>10210187
>t. brainlet

>>10204781
There is no upper boundary on the number of possible states, however. The number of real configurations of the universe is definable and finite, yeah, but the possible configurations/states are infinite because there is no upper limit to certain spatial dimensional attributes.

>>10210073
Mathematicians can only calculate numbers, and they are too often uneducated about anything else. For example, platonism indicates massive ignorance among mathematicians.

>>10210195
Sad

>>10210232
>t. brainlet

>>10210212
Mathematicians are most commonly more educated in the fields of epistemology and philosophy than other STEM professionals.
That most mathematicians are platonists is simply because the platonic realm is objectively real, and mathematicians accept this truth like they accept any true proposition.

In so far as infinity is a tool in which we may use, we use it to arrive at a finite conclusion. Should it pass that the result is itself infinite; we discard it and call it indeterminate. Irrational numbers exist, in the same way that the economy exists, that is to say, it is a human abstraction.

>>10203514
numNumbers = last [1..]

>>10203514
How long is a piece of string?

>>10207790
Finitists don't allow infinite objects so they wouldn't use naive set theory (because it allows unrestricted comprehension) or ZFC (because of AI).

Without going into details, a set theory that would satisfy a finitist (i.e., no infinite objects exist) can at best construct all of the integers, but cannot show that there exists a set that contains all integers. That is, the integers if such a notion exists would be a proper class under any acceptable version of finitism.

To finitists, why do you have a problem with simply expanding the definition of a sets size when we encounter the size of the natural numbers, when it clearly allows insights in other fields of mathematics?

>>10210323
>Mathematicians are most commonly more educated in the fields of epistemology and philosophy than other STEM professionals.
Not sure what maneuver is that, but in practice that level is still indiscernible from zero. Which is perfectly expected, because mathematicians don't need philosophy to calculate numbers.
>That most mathematicians are platonists is simply because the platonic realm is objectively real, and mathematicians accept this truth like they accept any true proposition.
That's how delusions work.

Newfag here, so are finitists like the /pol/ of /sci/?

>>10203783
>>10203887
>>10204181
>>10207464
>>10209769
>>10210426
>>10210522
...so...

how many integers are there?

>>10210668
You have a set of all integers
Take the largest integer, add 1, and add it to the set
Contradiction
QED

>>10209967
it's supposed to look like Rich Piano, if that helps you guess the board

>>10210661
Pretty much, infinitism is basically latent craving for BBC.

>>10210670
Of course, therefore there are infinitely many integers. What's so difficult for finitists to understand?

>>10210668
see >>10208823

>>10210668
More than 2.

>>10210677
Yes I have seen that and I did get quite close to letting out a sensible chuckle when I first saw it. It's not quite as funny anymore though

>>10210682
infinity is more than 2. Can you give me a strict upper bound on the size of the integers?

>>10203514
an infinite amount

>>10210685
You can't define operations for infinity, because infinity doesn't exist.

>>10210809
sure, can you give a strict upper bound on the number of integers?

>>10210809
Wrong. Infinity is the only thing that exists.

>"Finitists"
Is this some new flatearther-like thing I'm getting in on the ground floor of making fun of?

>Strict upper bound on the number of integers +1

>>10210650
>mathematicians don't need philosophy to calculate numbers.
Calculating numbers is what sciencelets do, not mathematichads.

>>10203514
Integers are as real as infinity. If one exists, so does the other.

>>10208802
>give me (i.e., CONSTRUCT)
You mean RETRIEVE
you are not "constructing" it, you are "retrieving" it from the platonic realm

>>10203514
Is anyone REALLY TRUTHFULLY a finitist?
Like, I don't believe in bigger and smaller infinities, but who doesn't believe in infinity itself?

>>10212534
Now that's what I call autism

>>10212567
your ableism is not allowed on 4channel go back to 4chan
also im not autistic

>>10212534
>I don't believe in bigger and smaller infinities
>I don't believe in a mathematically proven theorem
en.wikipedia.org/wiki/Cantor's_theorem

>>10212572
Meant for >>10212558

This thread in one pic.

>>10212558
>believe in infinity
>>>/x/

And still not a SINGLE real answer for the OP question

>>10203514
Question for finitists

If you deny Infinity why not Zero as well?

Clearly you can never actually find a zero but only get arbitrarily close to a zero as 0 = 1/∞
Zero is only the limit of an infinite amount of approximations but not actually existent in reality,

exactly AB integers

>>10212572
There is only one infinite set,
as all infinite sets have the same cardinality

It doesn't matter whether we go "hurr because I say so this number Ë comes after the last number in this infinite set" that's talking about ordinality and when we talk about bigger and smaller we are talking about cardinality, aka the number of numbers in a set
And if that set includes no 'number' of numbers but rather 'endless' numbers, it is just that

>>10203514
Fuck you for asking this. I fucking hate you.

There's... a lot of 'em but... you... YOU CAN'T PROVE INFINITY. So. Show me something *in nature* that is infinite.

You can't!

>>10213799
>something *in nature* that is infinite.
>You can't!
non-issue, nobody gives a fuck
go back to playing with legos, math isn't for you

>>10213669
construct a bijection from the reals to the integers and then maybe I'll listen to your retarded ramblings

>>10213799
If for any integer there is a greater integer then there are infinitey many integers

>>10214069
n=infinity

>>10203514
None. They're an abstraction, they don't exist.

>>10203514
3.

>>10212840
Don't give them any ideas

>>10203881

>>10209967
The Piano's axioms.

>>10214066
constructivists literally believe there's a surjective mapping from the reals into the integers

>>10210058
>>10210211
We don't know either of that.

>>10213799
what exists beyond the edges of the universe?
you're right I can't prove one way or another, just curious what you think might be there if you don't believe in the idea of infinity

>>10214472
*injective

>>10214588
Let [math]\phi[/math] be the function that assigns each real number to a program that enumerates its decimals. Then let [math]\pi[/math] be the function that assigns to each program an integer representative of its source code in any encoding. If [math]x \in \mathbb{R}[/math] then [math]\pi\circ\phi(x)[/math] is an integer and this function is clearly injective as each integer, once decoded as a program, corresponds to a single program.

>>10210212
Hi /lit/ :^)

>>10212840
Pretty sure there was a period in history when this was a topical argument.

>>10214709
Ha, this is neat. For people who are interested, the problem with this approach is that with 100% probability any real number you choose can't be given a finite description and if you don't have a finite description then you don't have a finite program and the only programs that can be encoded as integers are finite programs. In other words, only a countable proper subset of the reals (that contain the algebraic numbers as a proper subset) are actually definable. The remaining undefinable reals are just that, undefinable. That means that any real number you can describe is definable and the undefinables are pretty much unthinkable numbers and only "exist" as an abstraction that you can't produce any examples of.
While I personally believe the justification for believing the reals "exist' is tenuous I don't personally have anything against them as an abstraction in the same way I don't have anything against using the hyperreals instead of the reals whenever it makes things more convenient.

>>10214709
define "program" in this context and prove that such a program exists for each element of R

>>10214776
Not that guy but
>define "program" in this context
This is pretty standard computability theory
>prove that such a program exists for each element of R
This is the problem, or more generally the issue is as described here >>10214775

>>10214775
>any real number you choose can't be given a finite description

but some irrationals can be computed to an arbitrary accuracy, like sqrt(2) using newtons method, right?

isn't the existence of phi the problem here?

>>10214823
>but some irrationals can be computed to an arbitrary accuracy, like sqrt(2) using newtons method, right?

or are there no numerical methods that can actually do this for a given number?

>>10214823
>>10214828

i guess this is a question of whether the size of the program grows with the degree of precision.

>>10214823
>but some irrationals can be computed to an arbitrary accuracy, like [math]\sqrt{2}[/math] using newtons method, right?
[math]\sqrt{2}[/math] is an irrational that has a finite description. Same as [math]\pi[/math]. The rule of thumb is that
>if you can give a finite description of the real that tells other people exactly what real number you're talking about (even if you can't compute its digits) then it is a definable real.
For instance,
>let [math]r=0.1011011101111011111\ldots[/math]
would arguably qualify as a finite description for a number because you can see the pattern in the digits and you know exactly which real number I'm talking about.

>>10214823
>isn't the existence of phi the problem here?
No. [math]\varphi[/math] can be computed.
https://en.wikipedia.org/wiki/Golden_ratio#Calculation
More generally, any real number for which you can produce an algorithm or write a formula that will spit out it's digits (even if the program would have to run for an infinite amount of time because of an infinite amount of digits) is a defineable real (it's actually even a computable real see picture of >>10214775 ). That said, you don't even have to be able to compute the digits of a real number in order for it to be definable. You just have to be able to give a finite definite description of it.

>>10214831
No. The issue is that every undefinable real number (i.e. almost every real number) lacks a finite description. It's something like:
>The only way to actually describe the number is to give an infinite list of all of it's digits.
You might be able to come up with shorter descriptions that use mathematical properties or patterns in the digits but if it's truly an undefinable then no matter what description you come up with it will always have to be infinite.

>>10212807
See >>10210090
Not that finishits have an answer, of course.

>>10213669
>There is only one infinite set
>set of even numbers = set of odd numbers
Retard.
>as all infinite sets have the same cardinality
Wrong by a proof so simple even a middle-schooler can understand it:
en.wikipedia.org/wiki/Cantor's_diagonal_argument
>when we talk about bigger and smaller we are talking about cardinality
Cardinality is exactly what Cantor's theorem is about you mongoloid.

>>10214709
This only works for computable real numbers, which are countable precisely for the reason you stated.

>>10214882
I think most finitists are avoiding this thread because of the huge amount of shitposting non-finitist undergrads.

>>10210090
There are people working on other ways to count infinite sets aside from the Cantorian way. See:
https://www.cambridge.org/core/journals/review-of-symbolic-logic/article/measuring-the-size-of-infinite-collections-of-natural-numbers-was-cantors-theory-of-infinite-number-inevitable/325464FFF1E318E3E51A80E652FA1C5B
Finitists accept an infinite set of naturals. I believe ultrafinitists allow a finite but arbitrarily large natural.

>>10214852
To add to this, it does not matter if your finite description is in formal language or English prose or in any language over a finite alphabet (eg. LaTeX, UTF-8, ..., pretty much all human languages). The number of finite sentences will always be countable and almost all elements in any uncountable set are impossible to explicitly define.

>>10214918
>finite but arbitrarily large

>>10215003
As in any natural that you need you can have but you don't have the entire set. Basically thinking of the act of producing naturals as a process so that you can obtain any natural in finite time but never the entire set.
Of course, there are people who will argue that certain naturals are too large to be representable in the real world and therefore act as an upper bound (but not a least upper bound).

>>10214775
puts("???");

>>10212807
Infiniggers are just in denial, because they are religious fanatics.

>>10215053
>bringing time into mathematics that has nothing to do with time
>"producing" (whatever the fuck that means) natural numbers instead of just using them
>bringing "the real world" into mathematics for no reason

>>10215579
>time
It's an analogy for dum dums like you who.

>>10210065
That's a lot of coin flips. Please exhibit this number to me.

>>10215619
an analogy for what, retard?

>>10215053
>your brain on finitism
Embarrassing.

>>10215701
What do you mean by "exhibit"?

>>10214918
>There are people working on other ways to count infinite sets aside from the Cantorian way.
>Unwittingly, Cantor shows in this passage how his solution to the Galilean paradox
leaves one of our intuitions about infinite sets without proper explication.
Wow this is really dumb. There IS a proper explication for this intuition, and it's called being a subset.

if I have 1 apple and I take a bite out of it, do I still have 1 apple?

>>10214918
>We thus see that whether the even numbers have the same numerosity as the odd numbers
will depend on the choice of ultrafilter.
lmfao

>>10216060
oh ok I guess all the finitists have to bring to the table is huge quantities of wut

>>10216068
It's the same principle used in the construction of the hyperreals. You're literally a brainlet if you don't get it.
>>10216048
lmao

>>10215985
>>10215978
See: computability theory

>>10214775
>with 100% probability
xorshift128+ definitely has finite code.

>>10215988
You can for example, record a video of yourself flipping a coin 2^100 times. Or you can show me how to construct the number from Peano axioms. That'll be a lot of succs, so you better get started soon. I can begin with a few just to help you out: 2^(2^100) = succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ succ ...

>>10216581
Even RNGs can only produce a countable number of values.
>>with 100% probability
https://en.wikipedia.org/wiki/Almost_surely

>>10203514
More integers appear if you investigate them more, they are in the beyond in fog distance and are discovered and rendered only if you get close, they do not exist until then. They require platonic ideal world to exist and it happens only if you examine some thinking, therefore integers don't even exist until you imagine them, it's hard to count all existing integers in universe. Same goes for real, they just don't exist until you make them so.

>>10216672
The dude suggested to select numbers at random, hence RNG.

If you asked to pick a random number there is near 0 probability to pick number you can't describe, therefore integers are limited by means of description.

>>10214852
Is there a proof that an undefinable number exists? The method to find such number would itself be the definition.

>>10216894
Even then, the method by which you chose said value would give you a definable number (you could always describe the algorithm and seed values to do so).

>>10216914
As far as I know there is none for exactly the reason you stated.