/sci/ - Science & Math

[Anonymous No.14970101]

>assume infinity exists
>then there is an infinite number of positive integers and something can be done an infinite number of times
>take 1 and put it inside of a box and then take out 1 because it is the square root of 1
>take 2 and put it inside of the box
>take 3 and put it inside of the box
>take 4 and put it inside of the box and then take out 2 because it is the square root of 4
>....
>take n and put it inside of the box and then take out k if it is the square root of n
>do until n = infinity
>each time, you either put a number in the box or you put a number in the box and take one out
>therefore each time you either increase the amount of numbers in the box by 1 or by 0
>for any number, no matter how high, there still exists a chance that it does not have an integer root
>therefore the amount of times the number of numbers in the box increases by 1 is infinity
>therefore after n = infinity there must be infinity numbers in the box
>however every integer is a square root as it can be squared
>therefore there must be 0 numbers in the box
>this is a contradiction
>therefore infinity cannot exist

[Anonymous No.14970136]

>>14970101
mmp embraces the paradox of the infinite nothingness by lensing it through the ideas of precision at length. Nothingness, the zero, is perfect precision at no length, while infinite is no precision at endless length. Together combined they birth the continuum, the notion of unity, magnitude and than thus number

[Anonymous No.14970140]

i watched that stand up maths videos too, unlike you i didnt get filtered nigger

[Anonymous No.14970141]

>>14970136
formally, the construction of the continuum is represented by the 'illuminati operator' which bequeaths the holofractal unity

[Anonymous No.14970330]

>>14970101
>>then something can be done an infinite number of times
prove it

[Anonymous No.14970376]

>something can be done an infinite number of times
Usually mathematicians don't assume this, they generally use infinity only to make infinite sets.

[Anonymous No.14970386]

The thing about supertasks (doing something an infinite number of times) is that it's usually underspecified. You have a rule that tells you how to go from state n to state n+1, and so given a state 0 you can compute the state at any natural number n. But what is the state at infinity? If at some point the state stops changing, it would make sense to use that state, but that doesn't always happen.

[Anonymous No.14970449]

>>14970101
>babby's first "process vs limit"
"The sequence 1/n is positive but its limit is 0, oh no!!! Contradiction!!!!"

[Anonymous No.14970533]

[math]1/n > 0[/math] but [math]1/n \to 0[/math] and [math]0 \not> 0[/math] oh no!
or more generally [math]a_n > b[/math] and [math]a_n \to a[/math] does not imply [math]a > b[/math]
but [math]a_n \geq b[/math] and [math]a_n \to a[/math] does imply [math]a \geq b[/math]
and in general if S is a closed set then [math]a_n \in S[/math] and [math]a_n \to a[/math] implies [math]a \in S[/math]
now what can this tell us about supertasks?

[Anonymous No.14972009]

>>14970136
>>14970141
least retarded person on this entire thread

>>14970140
he literally disproves the existence of infinity by showing that there is a contradiction of 2 logical arguments then says that one of them is false because... because it just is okay???? having basic critical thinking skills is not getting filtered retard.

>>14970330
map all of the steps of the process to an integer. as there are infinite integers, there can be infinite steps of a process. the existence of 923565325698235 and the fact that it is unique to all other integers means that the state of things at the 923565325698235th step exists and can be represented by 923565325698235.

>>14970376
well then thats retarded

>>14970386
"infinity" does not exist. if it did there would clearly be a contradiction between what it approaches and what it "is at infinity". imagine if a series approached 1, as in its limit was 1 but "at infinity" it was 2. its a contradiction. there is no "at infinity", there is no "infinite set".

>>14970449
>>14970533
retards i know what a limit is. the limit of the amount of numbers in the box is infinity yet "at infinity" the amount of balls in the box is 0. that is a contradiction.

[Anonymous No.14972035]

>>14970101
Infinity doesn’t exist. Zero doesn’t exist. Negative numbers don’t exist. Decimals don’t exist. The highest number is one hundred.

[Anonymous No.14972040]

>>14972035
What about 96?

[Anonymous No.14972041]

>>14972009
>imagine if a series approached 1, as in its limit was 1 but "at infinity" it was 2. its a contradiction.
That's not a contradiction, it just means the function isn't continuous at infinity.
Imagine if a function f(x) approached 1 when x approached 2 from the left, as in its limit from the left was 1 but "at two" it was 2. Would that be a contradiction? Because that's just the floor function.

[Anonymous No.14972044]

>>14972040
You mean 2(12^2)/3?

[Anonymous No.14972046]

>>14972035
The highest decimal number on 4chan /sci/ is 10 * (10^1999 - 1) + 9. Arbitrary size numbers don't exist, there is always a limit to the number of digits.

[Anonymous No.14972056]

>>14972046
its 10^2001 -1

[Anonymous No.14972061]

>>14972056
Do you mean 10^2000 - 1? There are 2000 characters available. But you have to be careful about integer overflow!

[Anonymous No.14972063]

>>14972041
>the function isn't continuous at infinity
say that to yourself, in your head a few times then tell me if it makes sense.

[Anonymous No.14972064]

>>14972063
It makes sense.

[Anonymous No.14972065]

>>14972061
nvm yes youre right

[Anonymous No.14972069]

>>14972063
More constructively, did someone tell you some not-even-wrong nonsense like "infinity isn't a number, it's only a limit"? Infinity as we use it in calculus class is not a member of the real numbers, but it is a member of the extended real numbers, which consist of the real numbers, infinity, and negative infinity.

[Anonymous No.14972083]

>>14972063
it makes perfect sense. where's the problem?

[Anonymous No.14972090]

>>14972009
>least retarded person on this entire thread
thank you, it is rare to receive a compliment here.

MMP hopes to clearly demarkate the distinction between the etymological definition of 'real number' and the modernist joie de vive definition 'real number' by consolidating them both under a single model birthing a notion of the continuum that can mode switch between the two

[Anonymous No.14972092]

>>14972083
it doesnt make sense but its logically consistent so you win

[Anonymous No.14972104]

>>14970101
This is a valid proof that infinity doesn't exist.

[Anonymous No.14973167]

>>14972104
i read the thread and youre fibbing

[Anonymous No.14973171]

I've always wondered what pythagoras would think of modern math if we somehow could bring him into the future.

[Anonymous No.14973571]

>>14973167
How does it not disprove infinity?

[Anonymous No.14973576]

>>14970376
how exactly do you check that a set is an infinite set?

[Anonymous No.14973889]

>>14970101
You cannot reach infinity with an algorithm. Take some axioms that say infinity exists and prove they don't work with each other.

You will not because there are no such axioms (to my knowledge). Instead you will get infinity classes and stuff, but not infinity as an arithmetic number.

In short: Infinity is a property, not a number.

Good luck destroying ZF(C)

[Anonymous No.14973903]

>>14973889
>Good luck destroying ZF(C)
There is nothing to destroy. The emperor has no clothes.

[Anonymous No.14974190]

>>14973576
You can prove a set is infinite by assuming the size is a natural number and arriving at a contradiction. For example, the set of natural numbers is infinite. Assume to the contrary that the size of the set of natural numbers is itself some natural number n. The natural numbers from 0 to n have size n+1, so [math]n \geq n+1[/math], which is a contradiction. Therefore the set of natural numbers is infinite.

[Anonymous No.14974193]

>>14973889
Never heard of the surreal numbers?

[Anonymous No.14974281]

Let's say you do set theory and the axiom of infinity is adopted.
Now list set theory axioms in order of the reasonability.

[Anonymous No.14974446]

>>14970101
I can out-Wildberger that.
Assume infinity exists.
It follows immediately from this assumption that any proof by contradiction purporting to show the nonexistence of infinity is flawed.

[Anonymous No.14974575]

>>14970449
Don't even bother, anon. There are retards on this board who will swear up and down that, why yes, of course they know that in real analysis, infinity isn't an actual magic number -- that it's just shorthand for "goes arbitrarily large finitely" -- and, why yes, of course they know that in real analysis, the = sign sometimes means only "can get arbitrarily close to without actually reaching." Yet the same retards will mouth-breathe all over the board in ways suggesting that they don't actually understand these things (convergent sums are a particular disaster with the allure of the = sign).
Some people are ultrafinitists not because they're thoughtful math meditators like Wildberger but probably because they have to be to save their bruised egos from failing their real analysis classes through not being able to grok and internalize some fundamental concepts.
inb4 fedneck replies

[Anonymous No.14974592]

>>14974575
>thoughtful math meditators like Wildberger
Of course in the same sense that that Theranos blondie proved a thoughtful medical science meditator.

[Anonymous No.14974617]

>>14974281
The trouble with maths is that it constructs random axioms with no regard for reality.
Take Set Theory. How does it take into account the properties of actual sets?
Wildberger has pointed it out ad nauseum.
What does Set Theory have to say at all about television sets? Sets in tennis? Movie sets? Sets in poker?
It has lost any connection to the reality of peoples.
What maths ought to do is to stop making up "axioms", and instead try to absorb the reality
of the real world around us. To describe what is out there, and leave it at that.

[Anonymous No.14974622]

>>14974575
Well, can you explain how does OP not prove that infinity doesn't exist?

[Anonymous No.14974626]

>>14972083
>>14972064
The definition of continuity implies the function is DEFINED at the point. A function cannot be defined at infinity because it's not a fucking number

[Anonymous No.14974628]

>>14974626
a function's inputs have to be numbers?

[Anonymous No.14974630]

>>14970101
Infinity only exists in God. In Christian Theology, 'paradise' or the world after the second coming is literally endless and ceaseless, infinite becoming with God an all of creation forever and ever and ever. It's going to be a HUGE adventure. That is, if you repent and give your heart to God. There is no other way. What we know of the universe is but a spec of sand compared to His infinite magnitude and glory.

Consider space infinitely expanding: God is so powerful, that he can literally create space. Mind boggling to think about, really.

[Anonymous No.14974635]

>>14974622
>can you explain
Precisely define "do until n = infinity" and "after n = infinity."

[Anonymous No.14974641]

>>14974635
suppose it takes 1 second to perform the 1st step.
suppose it takes 1/2 second to perform the 2nd step.
suppose it takes 1/4 second to perform the 3rd step.
etc.

>do until n = infinity
do until 2 seconds have passed

>after n = infinity.
after 2 seconds since you've started

[Anonymous No.14974642]

>>14974635
not doing your philosophy homework

[Anonymous No.14974644]

>>14974641
>>14974642
I'll await a rigorous definition of "do until n = infinity" and "after n = infinity." Not doing your real-analysis homework.

[Anonymous No.14974647]

>>14974641
2 is a number.
Infinity isn't a number.
Don't blame him for not wanting to waste many words on you retards.

[Anonymous No.14974651]

>>14974644
what about what I've just written did you not understand?

[Anonymous No.14974657]

I hate infinity and set theory ffs
Such a hard subject for what is essentially bullshit

[Anonymous No.14974664]

>>14974651
The fact that you're a retard who thinks 2 is ever actually reached when you see the convergent sum ∑ (1/n) = 2. It's what I was saying in >>14974575 about how some retards get confused by the = sign in real analysis.
I know from past experience that there's simply no getting over this low-IQism on the part of some people.

[Anonymous No.14974670]

>>14974575
no one who is actually able to go past middle school can fail a math class in an American university. Just save yourself the embarrassment and address the issues instead of trying to ad hominem all day long.
Students who struggle never stop to question what they're being taught.

[Anonymous No.14974682]

>>14972035
QUINTUPLE WRONG. One and zero exist. All other numbers do not exist. Except eight because there are eight bits in a byte. Ignore the eight.

[Anonymous No.14974686]

>>14974664
So, can you explain how does OP not prove that infinity doesn't exist. Suppose the conditions in >>14974641. What do you think will be inside the box after 2 seconds?

[Anonymous No.14974728]

>>14974686
That anon up there who said:
"The sequence 1/n is positive but its limit is 0, oh no!!! Contradiction!!!!"
Do you think 0 is actually reached? If not, why would you think that 2 is actually reached in ∑ (1/n) = 2? The only difference is that the first case is an infinite sequence and the second case is an infinite series, but the meaning of infinity and convergence used in each case is the same: "By taking n high enough, I can make this sequence (or series) have as small of a nonzero gap from 0 (or 2) as you like." You're still dealing with finite numbers, arbitrarily large, not some magical number called infinity that you set n to make 1/n suddenly become 0.
Best I can do for you retards, I'm afraid.

[Anonymous No.14974732]

>>14974682
>One
>zero
Neither of those are numbers. Two is the smallest number. If someone said they had a number of tasks to do, would that be true if they had one task to do? No tasks to do? Of course not. One is not a number, it is the unit which numbers are composed of. The part is not the whole.

[Anonymous No.14974733]

>>14974728
>Do you think 0 is actually reached?
No

Can you answer the question now?

[Anonymous No.14974765]

>>14974641
stop reading pop-writer idiots who think that an idealized infinite series can model space and time, and then you won't ask meaningless questions.
there's your biggest problem. if you got this misunderstanding from reading about zeno's dichotomy paradox, as I suspect you did from the series involved, read more contemporary ideas about its resolution.

[Anonymous No.14974784]

>>14974664
that's a bit harsh because, for many years, that infinite series was thought to resolve zeno's dichotomy paradox -- until whitehead and others reminded people what "= 2" means for that infinite series in basic analysis

[Anonymous No.14975231]

>>14970101
Isn't this saying
>numbers can be squared so infinity doesn't exist
I don't see how the ability to square a number means you can't just keep counting forever, regardless of what this riddle is saying

[Anonymous No.14975934]

>>14975231
Its easier to see with a factorial rather than a square function since you can't count with factorials forever and you actually stop being able to even calculate the value after 170! let alone count to it.

[Anonymous No.14976886]

>>14970101
Is a number system defined as infinite on the basis you can cycle through the digits without bounds? Like running on a treadmill but ascribing a unique position to each second that passes while on it?

[Anonymous No.14977581]

>>14974732
>Neither of those are numbers. Two is the smallest number. If someone said they had a number of tasks to do, would that be true if they had one task to do? No tasks to do? Of course not. One is not a number, it is the unit which numbers are composed of. The part is not the whole.

This is actually kinda based/

[Anonymous No.14978778]

>>14975934
isn't that just a limit of certain calculators ? I more meant that you can count infinitely because there's nothing stopping you adding 1 to any number. Even if you wanted to name every '000 interval you can infinitely join letters together for names.

[Anonymous No.14978811]

>>14970101
>therefore after n = infinity there must be infinity numbers in the box
There is no such thing, retard. There is no "after".

[Anonymous No.14978979]

>>14978811
Why not?

[Anonymous No.14979102]

Wildberger plays against /mlp/ today in a few hours >>14979025

[Anonymous No.14979642]

>>14974446
>I can out-Wildberger that.
>Assume infinity exists.
>It follows immediately from this assumption that any proof by contradiction purporting to show the nonexistence of infinity is flawed.
I know you're joking, but this mindfucked me as a non-constructivist, and it took me way longer than it should have to identify the subtle problem in logic.