/sci/ - Science & Math

What's the highest natural number?

>>9334649
9

>>9334649
10 "triangle" 4 where "triangle" is the successor of exponent
he has videos on big numbers
you can check it

>>9334643
>justification for the axiom
That's not how axioms work.

>>9334671
Not really, there's a reason behind why we choose certain axioms.

numbers are hypothetical things. while mathematical principles exist in reality, numbers themselves are a construct of the mind. since infinity is rooted in numbers, then it too is hypothetical.

if you accept numbers, then you also must accept infinity.

however, you don't have to accept numbers.

>>9334681
the reason is that you make a lot of shit with little assumptions

if you don't have the axiom of infinity, you'll then have 20 other axioms. it's less efficient. hence wildberger is a brainlet.

>>9334649
[math]10^{200}[/math]

>>9334643
>You have 15 minutes to post any justification for the axiom of infinity or its equivalents.
The idea of a "largest natural number" is pants-on-head retarded. The alternative is infinite sets.

>>9334643

We haven't proven a contradiction from it yet. It's reasonable to assume there is none.

Stop telling me how to manipulate my symbols!

>>9334671
spotted the vulgar formalist

Proof by contradiction:
If infinity didn't exist, there would have to be a highest natural number
that's dumb

therefor infinite exists
qed

>>9335586
if you believe the mathematical universe consists of the hereditarily finite sets its perfectly coherent to say that infinity doesn't exist (i.e. any "infinite" collection is just a proper class) while still holding that arbitrarily large finite sets exist

The largest number is 4, you're just lying to yourself beyond that

>>9335600
So what you're saying is, "yes, I think there is a biggest natural number but it's arbitrarily large"

so what's that number +1?

>>9335609
You've activated my trap card!

>>9335610
>So what you're saying is, "yes, I think there is a biggest natural number but it's arbitrarily large"
No, he/she is saying that for every natural number n there is a set of size n, but that there is no set of all natural numbers.

>>9335610
>So what you're saying is, "yes, I think there is a biggest natural number but it's arbitrarily large"
first off, I'm not a finitist, I'm just playing devil's advocate

secondly, I'm not saying that at all. I'm saying that it's coherent to say "for every set there's a bigger set" without admitting that there's an infinite set

>>9335610
Undefined obviously.

>>9335616
>>9335624
>every set has a bigger set
This is literally just infinite regression. You're using infinity to avoid using infinity. Seems a bit ironic. Like you tried to get rid of something embarrassing by sweeping it under the rug but it's still sticking out
>we don't need an infinite set, as long as we have an infinite set of finite sets!

>>9335633
>as long as we have an infinite set of finite sets!
That's actually not the case

>>9335633
>>we don't need an infinite set, as long as we have an infinite set of finite sets!
It's more like we don't need a sets of all sets since we have a class of all sets. We don't need an infinite set of finite sets as long since we have an infinite class of finite sets

>>9334643
You have 1 second to post any justification why I should post a justification

>>9334681
Yeah, because if you choose them well, you can model lots of interesting things in the world with math. And the axiom of infinity is one of those good choices

>>9335655
>we don't need infinity if we just use infinity

you can't make this shit up

>>9334643
My justification:
Axioms don't need to be justified.

You have an eternity to show me the ZFC is inconsistent. I'm not waiting.

>>9335119
Usual forms of finitism don't claim there is a largest natural number.

>>9335757
>>we don't need infinity if we just use infinity
Who are you quoting?

>>9334643
Equilateral triangles exist. Circles exist.

>>9335577
We haven't found a non trivial zero of the zeta function that does not have real part 1/2, therefore I have proven the Riemann Hypothesis, according to this poster. I will be waiting my million bucks, and you better pay up. Don't worry, if you do not have enough money just tell your bank to apply the axiom of infinity to your bank account. I mean, you say it is true and it models reality right? So just apply it.

>>9335616
>he/she

t. reddit

The largest number depends on how you write numbers
[math]1_2[/math] = 1
[math]2_3[/math] = 2
[math]7_8[/math] = 7
[math]9_{10}[/math] = 9
F[math]_{16}[/math] = 15
[math]M_{roman}[/math] = 1,000
[math]M_{greek}[/math] = 10,000

For any arabic number system, it is the base n-1.
>Base10 ~> 9

[math]1000_10[/math] is not a number. It is one zero zero zero, where one and zero are the numbers. It is "one thousand" 1's, and defines a "number of" 1's. Or "one hundred tens". 1000 is only a number in greco and roman numerals.
There is a difference between a number and a "number of" things, and subhuman failure to acknowledge this difference is what leads to asinine "higher" maths usage of [math]\infty[/math] as a number capable of defining a limit or methods involving infinitely progressive arithmetic.
[math]\infty[/math] + 1 = [math]\infty[/math]
[math]\infty[/math] × 2 = [math]\infty[/math]
[math]\infty[/math] × [math]\infty[/math] = [math]\infty[/math]
[math]\infty[/math] + [math]\infty[/math] = [math]\infty[/math]
[math]\infty^{\infty}[/math] = [math]\infty[/math]
proper, intelligible results cannot be evaluated from [math]\infty[/math] without a number base[math]\infty[/math], for example
[math]\infty_{\infty}[/math] + 1 = [math]10_{\infty}[/math], but because infinity is not even remotely close to defining a limit, this system would simply assign every conceivable number it's own representative symbol with new symbols being created every minute of every day, and [math]10_{\infty}[/math] would not ever be written outside of users of that base system attempting to define an abstract concept much like users of modern numerology use [math]\infty[/math] to encapsulate an abstract concept.

>>9334683

I don't agree with that. Certainly numbers are hypothetical, but that doesn't force us to accept all forms of numbers if we want to accept "numbers" in general. There are plenty semi-obscure fields of math that use numbers which other mathematicians don't use. Such as the hyper reals, the p-adics, etc. That's not to say that other mathematicians reject these numbers; they don't say "these numbers aren't real" because any decent mathematician agrees that numbers are constructions. But they can say "these numbers aren't useful or interesting and so I choose not to acknowledge them.

A good example if the number 1/0. Most mathematicians work in areas where this number is forced to be undefined. however, hyper-real analysts might say "no, it's a number", but the other mathematician says "not in my domain".

So, in brief, I reject your assertion that infinity must be accepted simply because it is "theoretical". With this argument we would have to accept any sort of outlandish number system, most of which have little or no use whatsoever.

>>9334643
Statistically speaking, the only way for life to exist, is if one of the variables is infinite.

>>9335871

....not true...

With it, I actually do stuff that's useful for humanity.

>>9335895
No you dont. If you were actually doing something useful with maths, you would be using computer sciences, and if you were calculating numbers with computers, up to 15 decimal places of accuracy would be your general working methodology via floating points, or 64-bit long integers of whole numbers up to 9,223,372,036,854,775,807

15 decimal places of PI in most cases is accurate enough to visualize and give a workable result when PI is evaluated; but the point is that there are defined hard limits of maths in computer science and engineering that realistically prevent infinite values from being usable or useful, and since these fields are the real work productions of maths presenting solutions to problems that help people, claiming to use infinty as a helpful tool is nothing but a bold faced lie.

>>9335577
Consistency alone doesn't justify anything.

>>9335911
How's this ambition for indie game development, high schooler?

The unlimited capacity for infinity response exists in the Unqualified Absolute.

>>9335911
You don't need to store an infinite amount of data in order to use infinity in a program.
Here's a Haskell implementation of the Sieve of Eratosthenes:
> primes :: [Int]
> primes = sieve [2..]
> sieve :: [Int] => [Int]
> sieve (p : xs) = p : sieve [x | x <= xs, x `mod` p ≠ 0]
The function is based on an operation applied to the infinite set [2..]. It has no finite ceiling built into it. You can take however many of the infinite set of primes you want from that function. Just because your machine will only be able to take a certain number of records from that function given a certain amount of runtime due to its own limitations doesn't negate the fact that the program itself is operating in terms of infinite sets.
It wouldn't help any to rewrite that program in terms of some explicit finite upper limit. You would get no performance gain by doing so and would actually make the logic less clear by adding an unnecessary "largest number" check. And worse than that, you would no longer have an accurate function for values over your arbitrary ceiling.

>>9334643
Axioms are hypothetical premises.
If I tell you "suppose the Axis powers won WWII," you wouldn't be raising a coherent objection by saying they didn't actually win WWII. The point of a hypothetical premise is to explore what would be true given that starting premise. Whether the premise is true, false, or indeterminate is irrelevant since you can still get use from exploring what would be true given that premise.

>>9335979
>Just because your machine will only be able to take a certain number of records from that function given a certain amount of runtime due to its own limitations doesn't negate the fact that the program itself is operating in terms of infinite sets.

Yes it does. Infinity has no beginning and no end.

>>9335996

this

>>9336005
Neither does the infinity in that function.
You seem to be confusing forms with the objects that participate in them.

>>9336005
>>9336019
Actually, let me clarify:
Apply my response to your bit about "no end," but as far as "no beginning" goes you're just wrong, infinite sets definitely can have beginnings.

>>9335979
Even if you wanted to use primes for cryptography, the mere admitting of using primes for cryptography immediately betrays any intentional security feature - so again no, you are not actually helping anyone by using something related to infinity. You could make an argument that a program may run indefinitely so long as a computer is powered, and that the program may perform innumberable actions so long as its indefinitely running, but this is not to be misunderstood as thereby using infinity as a tool of arithmetic. The computer does not have infinite memory registers and must discard, feed out, or replace certain information as time advances. It is more akin to a train with N amount of cars riding a railroad that is infinitely being laid ahead of it where the railroad line defines sequential numbers and the train+cars define the access and storage area. Infinite access or a train with infinite passenger cars would never fully leave the trainstation represented by real 0, thus it would not have been beneficial to ever board that train to reach a destination much less enjoy a ride because your passenger car never leaves the station - ergo incalculable. If we change the access to be limited, there is now a train with defined cars that can entirely leave the station, and although you may never get to the destination, at least you could enjoy the ride.

To say that discovering primes is the only useful method of cryptography is horseshit brainletism though. There are more than plenty of different complicated methods to encode and decode information.

>>9336027

If there's a beginning, it's not infinite, because there must be an end. You can't have one without the other. It's like saying you can have up without down.

>>9336045
You're confusing the function with a given instance of applying the function.
The former has nothing to do with machine limitations and is in fact written in terms of infinite sets.
Also I'm not that other guy who said he does useful things with infinity. I just wanted to show you that your assumption about programming not involving infinity was wrong.

>>9336052
The set of positive integers has a beginning and no end. The set of integers has no beginning and no end. You can have either case.

>>9336064
>The set of positive integers has a beginning

What beginning?

>The set of integers has no beginning and no end.

Then it cannot be a set. Sets require a beginning and an end.

>>9334643
it just werks

>>9336076
>What beginning?
1

>>9335839
He said reasonable not rigourously true

>>9335609
but 5 is a part of you

>>9336089

Can 1 exist without 0?

>>9336112
>Can 1 exist without 0?
Yes

>>9336112
>>9334745

>>9335818
Wildberger is finitism on retard steroids

>>9336114

And where's your reasoning?

>>9336140
Observe

[math]\{1\}[/math]

>>9334649
However many atoms exist, noting more than that can really exist outside of mental sophistry

>>9336158
>However many atoms exist, noting more than that can really exist outside of mental sophistry
What about however many quarks exist?

>>9336158

>>9336158
It takes way more sophistry to pretend the concept of infinity doesn't exist and to introduce twenty other axioms to recreate the mathematics we already had, gaining nothing except the ability to say "I didn't use infinity."
Also, if infinity had no existence in the physical world in any sort of way (which I doubt, but let's say that's true for the sake of argument), this would just make the mathematical concept of infinity even more valuable since it would allow us access to ideas we wouldn't have access to if we limited ourselves to shallow physical world specific arithmetic.
The whole point of mathematics is extending the scope of what we can think about, using abstraction to move beyond the limitations of mindless, purely instinctual non-human animals. That a given mathematical idea doesn't exist in the real world is a feature of the system, not a bug.

>>9336158
The universe is infinite with infinite matter. Get rekt wildassburger.

>>9336108
>some sperglord

spoiler most of the people on numberphile are celebrities (who have math degrees) under different makeup/lighting conditions than you're used to seeing them and using their hometown dialect

in
cog
neato

>>9334649
The number of planck lengths possible in the largest universe possible without repeating spacial events.

>>9336173
We haven't actually observed quarks with our natural senses so its nonsensical to assume they exist, by induction we must limit the naturals at the atoms. QED

>>9336427
Define "observe."
Even atoms haven't been "observed" if you mean seen through light reflecting off of them and into our eyes.

>>9336427
>We haven't actually observed quarks with our natural senses
Speak for yourself.

>>9336427
Everything we observe is made of quarks so yes we have.

>>9336422
what about fractions of planck lengths?

>>9334643
It's a placeholder for numbers we haven't managed to count to yet. But now that we've come up with the placeholder, we've stopped actually counting. It's a shame.

>>9336304
Just because we could not count it doesn't mean its infinite.
Thats why the concept of infinity is stupid.

>>9336761
this is what rationalists believe

>>9335861
1/0 isn't a hyperreal number.

>>9336963
It's completely irrelevant to mathematics whether or not some real world phenomenon is infinite.
We can still work with the concept of infinity abstractly either way, and mathematics has never been an empirical science, the fact the real world does end up agreeing with what applied mathematical modeling would predict is nice and interesting but having real world applications was never a requirement.
By analogy, you're certainly able to use the concept of programming to create useful real world systems like a self-driving car, but that doesn't mean programming in general is limited to only facilitating operations which participate in the real world in a productive way.
In fact if you really cared about real world applications you wouldn't want to limit these abstract systems to only that which is immediately recognizable as practical in an applied way to the real world because you don't know which ideas will end up becoming useful in that way in the future.

>>9334643
>You have 15 minutes to post any justification for the axiom of infinity or its equivalents.
There as it least one mathematical concept -- the natural numbers -- which describes an unlimited amount of objects. Set theory is a mathematical model of concepts, which means this concept needs an infinite set.

>>9336963
Just because you have a tantrum doesn't mean the universe is finite.

>>9336143

Those brackets either side represent zero.

>>9337327
¿Are you getting surreal with me?

>>9334643
Infinity is my God. I have faith in Infinity.
Praise Infinity.
Praise ZFC.
Praise Natural Numbers, which there are Infinite.
Praise the Universe, which is Infinite.

>>9334643
I don't understand all of this bullshit, but I think you want me to prove that there is such a thing as infinity. To that I ask you a question?
>What is the absolute, measurable limit, of human stupidity?

so there is no rebutal of his maths?

>>9340871
4

>>9336773
the concept of space and distance breaks down below the planck length

ITT:My Probability Zombies From Infinity (Divine)

>>9334643
>the axiom of infinity
... the *WHAT* ?!

/thread
>suck it
you prolly don't even know what this is nevermind

Either way we have had this conversation more times than our combined lifetimes can count, even if we started from a fetus and stared only at ceilings counting like autist's. I'm just the only one who get's it. Death created time to grow the thing's it would eat. just like the greek's left pig's on an island to breed so they would have food on the way home.

>>9341915
Damn, what if we are food for aliens on their way home?

>>9336427
You can actually observe individual photons - your retina is actually *that* sensitive. So yes, we have literally observed particles.

How many particles are in the universe?

Well, there's an awful lot in empty space it seems.

So how much empty space is there?

...Also, why we're at it - how many minutes until the end of time? Days? Weeks? Centuries? Millenia? It's all the same answer.

>>9336389
What the absolute fuck?

>>9342689
someone post the episode with miley cyrus sperging out

also i wanna see your face when you realise snowden has been running a popular science channel for years

>>9334666
What about 10 "triangle" 5, oh bringer of Satan's Trips...

>>9342725
I was personally shocked when I realized Brady is actually Keanu Reeves wearing a fake beard

>>9334649
Whatever the highest one ever used is.

>>9342064
>Have you ever calculated an infinite sequence of digits?
Isn't there an entire field of maths dedicated to this? Something to do with convergent and divergent infinite sums?

*looses zeno's arrow*

>>9344935
Yes, Zeno, yes there is.

>>9336389
>t. Doctor sperg