Finitist autism

>platonism = religion
>finitism = atheism
>formalism = agnosticism

>platonism = religion
>finitism = atheism
>formalism = agnosticism
What the fuck.

True its a bad analog. I'm religious yet believe in finitism when it comes to math that produces real results. The issue here is that it's sorely implying "believing" infinite sets to work means is similar to "believing" religion to work, when in reality religion produces working results regardless if you "believe" while atheism aka lazy brainletism doesn't give enough shit to actually figure anything out towards the effect of either contradicting believe or supporting it.

The fact that, for example, certain weak solutions to the Navier-Stokes equation are unphysical implies that the continuum is in some sense physically real. If the continuum is physically real, then [math] \mathbb{R} [/math] exists beyond mere formalism.

The universe does not obey finitistic mathematics.

> finitist thought is more attractive to those with a computation background
/thread, it's comp """sci""" brainlets.

Comparing stuff to religion, atheism, etc. is dumb.
Your full of shit, maybe you got lost on your way to humanities department
Totally agree retarded
Get the fuck away from me you dumb finitist, you probably don't actually know what these words mean. Your brainlet mind can't handle words bigger than 2 syllables.

Damn, truth hurts, you sticken it to them.

So many people here believe that there opinion has some sort of value when they know nothing of the subject. Don't talk unless you know what your talking about, dont just sprout "math words" in strings without meaning to justify your (meaningless) opinion. Instead maybe read a book. I'm lookin at the finitists here and people like

a literally meaningless string of words

> there opinion
> your talking about,
> sprout "math words"

What are you trying to say? My grammar is bad?This is Veeky Forums, a part of the internet, no one care. You are exactly the kind of people I was talking about, you go on Veeky Forums to a math topic and correct people on their english instead of maybe learning some math.

[math]\infty[/math] is not a number
[math]n \rightarrow \infty[/math] cannot evaluate to a finite answer in finite time
[math]0.\bar{9} < 1.0[/math]
[math]0 \neq 0.\bar{0}1 \ngeq 0.\bar{1}_{base2} \ngeq 0.\bar{9}_{base10} \ngeq 0.\bar{F}_{base16} \neq 1.0[/math]
[math]N \geq 2 \rightarrow \infty; (0.\overline{N-1}_{baseN} < 0.\overline{N}_{base(N+1)})[/math]
[math]X = \sum{N%3=0}^{/infty} 0.(\frac{N}{3})_{baseN} × 3_{base10} = 1.0 \neq 0.\bar{9}[/math]
[math]0.\overline{N-1}_{baseN} = [/math] NaN

Keep going user. The irony of your posts is delicious.

[math]\mod[/math]

[math]\infty[/math] is not a number
[math]n \rightarrow \infty[/math] cannot evaluate to a finite answer in finite time
[math]0.\bar{9} < 1.0[/math]
[math]0 \neq 0.\bar{0}1 \ngeq 0.\bar{1}_{base2} \ngeq 0.\bar{9}_{base10} \ngeq 0.\bar{F}_{base16} \neq 1.0[/math]
[math]N \geq 2 \rightarrow \infty; (0.\overline{N-1}_{baseN} < 0.\overline{N}_{base(N+1)})[/math]
[math]X = \sum_{N mod 3 = 0}^{\infty} 0.(\frac{N}{3})_{baseN} × 3_{base10} = 1.0 \neq 0.\bar{9}[/math]
[math]0.\overline{N-1}_{baseN} = [/math] NaN

So you're saying the universe has infinite energy?

>computers can only deal with a finite amount of things
This isn't really true. If you believe that then humans can't either.
Lazy lists are one kind of way computers deal with the infinite.
A slightly better example is that most theorem proving languages will have a non-finite set construct.

Are you making fun of the finitists or actually believe this, thanks for proving my point exactly. You write down a bunch of nonsense to make it seem like you know shit, but you are really just a brainlet. Listen up, heres the key:

0.999... represents the number after "finishing" the sum 0.9+0.09+0.009... (and we can find a scheme for computing this in finite time, though this is not the point: first sum 0.9+0.09 in 1/2 second, then add on 0.009 in the next quarter, then add on 0.0009 in the next eigth etc.).

0.999...9 is always less than 1 if there are a finite amount of 9s but thats not what .999... denotes, it denotes the number that is the limit of that sum, which is 1.

Trying to make sense of the gibberish that is written about 0.999... in different bases:

First note that 0.0...1 is not a thing (unless we are talking about surreals but your brainlet doesn't understand what those are, even then no one defines it as 0.0...1).

While any 2 different bases converge at different "speeds" to 1, that does not mean they can't converge to the same thing, your argument can be used to show that the sequence 1,1,1,1,.. and 3,2,1,1,1,1,... don't converge to the same thing (which is absurd because they both converge to 1 because they both are 1).

As for the other lines of mess, I have no idea what they are supposed to mean.

[math]0.\bar{8}[math] must converge towards 0.89 if [math]0.\bar{9}[/math] converges to 1.

The fact of the matter is [math]0.\bar{9}[/math] is simply not a natural number. It can only be crafted using elements of infinite sets of directions, like [math]\sum_{n=1}^{\infty}\frac{9}{10^n}[/math]
And doesnt otherwise naturally occur during normal arithmetic.
[math]0.\bar{3} × 3 = 1.0[/math]
[math]0.\bar{1} × 9 = 1.0[/math]
[math]0.\bar{n}_{base(n+1)} is simply not a real number.
QED

[math]0.\bar{8}[/math] must converge to 0.89 if [math]0.\bar{9}[/math] converges to 1.0. Theres no greater number above [math]0.\bar{8}[/math] and less than 0.89 after all.

0.889 is less than 0.89
and 0.8889 , 0.88889, 0.888889
so what is the next biggest number past [math]0.\bar{8}[/math]?
[math]0.\bar{8}9[/math]?

0.9 repeating really doesnt equal 1.

Seriously how can we define the next biggest number for any repeating decimal, much less [math]0.\bar{9}[/math]?

0.8
0.81 is bigger but
0.801 is smaller than 0.81
0.8001 is smaller still
0.80001 is smaller still
0.800001 is even smaller
0.8000001 is there a pattern here?
cause to me it looks like
[math]0.8\bar{0}1[/math] would be the smallest number bigger than 0.8 and less than 0.81, but i guess notation of a significand after the repetition isn't allowed?
so how would it be possible to know that [math]0.\bar{9}[/math] should equal 1? rather, why should it equal 1 in all circumstances, when it is just as easy to say it doesn't even exist at all?

[math]0.\bar{1} + 0.\bar{8} = 1.0[/math]
>this is how the equation actually evaluates
[math]0.\bar{1} + 0.\bar{8} = 0.\bar{9} = 1.0[/math]
>this is how turdburglars evaluate it

[math]0.\bar{1} - 0.\bar{1} = 0[/math]
>this is how everyone evaluates it
[math]0.\bar{1} - 0.\bar{1} = 0.\bar{0}1 = 0[/math]
>but this is somehow too confusing for turdburglars even though its exactly what they do with [math]0.\bar{9} = 1[/math] in bridging a gap with an infinitesimal

convergence is just rounding and dont deny it, so c'mon put away the elementary school math and put on your thinking hat.

That is true, and when I first was writing my post I was going to mention this but I forgot. I would say that this is not a true handling of the infinite, it is analogous to the finitist in mathematics, using algebra to conceal infinite objects. For instance, considering the ring Q[sqrt(2)], which can be described in a purely finitist framework, despite what it "really involving" an infinitely precise notion of the "square root of 2", in this way, it is like lazy evaluation.

>implying I'm a finitist

no.

Your opinion is worth less than the pixels it's written with. This is /sci, not /x, and your vaguely worded mysticism doesn't wash.

But all humans do with maths is find finite ways of dealing with the infinite. That's why we use things like limits. I don't see what you want from a "true handling of the infinite" unless you're arguing that it is never really possible.

In the same way a finite human is able to reason about non-finite things such as "the set of natural numbers satisfying predicate p", finite computers can be used to reason about non-finite things. There's nothing we can do with maths that couldn't (theoretically) be done on a computer.

Pretty funny to use Q as your example field since I don't think ultra finitists would believe in it.

>QED
kek

...

With the usual ordering of [math]\mathbb{R}[/math]
there is no such thing as "the next biggest number"
Your arguments make no sense whatsoever.

>t. butt blasted atheists

finity works better with real world measurements where precision is arbitrarily limited by the tools at hand. Beyond that precision, acknowledging that something approaches infinity adds no information so it tends to be as frustratingly useless as things like intelligent design. This seems more of an engineering complaint versus an autistic one.

If you suffer from brainletism, then yes. Meaning requires room for thought.

It is a real number, because we sense it as a 1 in the physical world.

Define the difference between 0.0...1 and 0 pls

I guess 0.999.... is its own universe, that expands itself to the untangible border 1.

0.999... is just a different notation for [math] \lim\limits_{n \to \infty} \sum\limits_{i=1}^{n} \frac{9}{10^i} [/math]. This thing makes sense if and only if the limit actually exists. The limit actually exists and it is 1. 0.999... is not its own thing. It's denoting the limit of that series/sequence. If you want the definition of a limit, see en.wikipedia.org/wiki/(ε,_δ)-definition_of_limit#Precise_statement_and_related_statements.

Now back to the main topic.

*looses zeno's arrow*

I've been seeing this on the same finitist threads. How sad that the CS fags don't realize that Math extends far beyond their puny CPUs.

>cannot evaluate to a finite answer in finite time
But it can retard. This is basic Calc 1 shit, look up "Limits at Infinity" it'll be in one of the earlier chapters bc of how easy it is to understand.

>assuming [math] 0.\bar{0}1 [/math] exists
fucking disgusting

The easiest way to prove that 0.(9) = 1 is to use base 3 you brainlets. In fact the method is pretty general, in that for any rational number with an infinite periodic representation in base x there exists base y in which its representation is finite.

Uh no.
For every N modulo 3 limit to infinity, 1/3 in that baseN × 3 easily equates to 1.0.
In base3, 1/3 = 0.1
0.1 + 0.1 = 0.2
0.2 + 0.1 = 1.0

[math]0.\bar{9}[/math] is not a number in base 10, and truthfully [math]0.\overline{N}_{base(N+1)}[/math] is not a valid number in any base. Brainlets think [math]0.\bar{9}[/math] must exist though because [math]0.\bar{3} × 3[/math] seems to evaluate to it, but only cause brainlets dont understand that a number [math]\bar{N}[/math] is not related to a number [math]N[/math].
They incorrectly evaluate [math]0.\bar{3} × 3 = 0.\bar{9}[/math] cause they treat [math]\bar{3}[/math] to mean the same as 3, but with using that logic [math]0.\bar{3} × 4 = 1.\bar{3}2[/math], which having used the same exact logic to get [math]0.\bar{9}[/math], now returns the incorrect answer.

>My theory is that finitist thought is more attractive to those with a computation background, since computers can only compute up to finite precision, and can only deal with a finite amount of objects, both in memory and in principle.
Nah.
A) Most programmers don't know or care much about hardware issues like that. A minority are deeply familiar with both, but everyone else is either hardware or software, and software people are all about abstraction free from physical concerns.
B) Object oriented programming is literally applied Platonism e.g. you instantiate objects that participate in abstract blueprint classes.
C) The limiting factors you brought up aren't unique to computers, they apply to everything else too e.g. human thinking isn't any less limited than artificial computation, both are classically physical cause and effect based functional processes.
So if anything, I would bet the average programmer is way more sympathetic to a framework that uses infinities than one which tries to avoid them.

actually that example was a little wrong too
[math]0.\bar{33} × 4[/math] might evaluate to [math]1.\bar{3}2[/math]

a megabrainlette might see [math]0.\bar{3} × 4 = 1.\bar{2}[/math]

either way, treating [math]\bar{n}[/math] like it's natural number n results in the wrong answer, so [math]0.\bar{9}[/math] as a result from [math]\frac{1}{3}×3[/math] is a wrong answer too.

>Lazy lists are one kind of way computers deal with the infinite.
You can't represent an uncountable set as a lazy list.

>You can't represent an uncountable set as a lazy list.
natnums = [1..]
You now have the natural numbers in a Haskell list. It'll give you however many elements you need in a give operation through lazy evaluation. And no, it does still count, there are many examples of infinitie set manipulation handled this way in Haskell. It works no matter how much you don't like it.

Uncountable, not infinite.

>uncountable set
>natnums
cslets, everyone

But there are other ways to represent uncountable sets.
Lean for example let's you use a set membership predicate to define a set.

Doesn't that constrain you to constructible sets?
en.wikipedia.org/wiki/Constructible_universe

>haskell
oh boy the one language designed literally just to do abstract math and reinforce the concept that you're totally not doing something that is worthless.

This is why I love Haskell. Its higher barrier to entry helps keep the brainlets out.

I'm not sure (haven't done much set theory).
Can you give an example of a non-constructible set?

It doesn't matter if infinity is real or not- it isn't useful. Nothing humans have to deal with is infinite. It's just a concept that useless number pushers mess around with all day to no purpose.

And even if it is real, humans- who are finite beings- can't ever comprehend it. People pretend to comprehend infinity but no one can. So once again, it is useless to even talk about infinity.

>It doesn't matter if infinity is real or not- it isn't useful.
>it is useless to even talk about infinity.
>calculus is useless
>analysis is useless
>I'm retarded

>People pretend to comprehend infinity but no one can.
Are you fucking autistic? Are you stuck in the 19th century? Mathematicians deal with infinities and prove theorems about them all the time, you worthless sack of shit. Just because YOU are too braindead to understand these concepts doesn't mean everyone else is.

Name me one example of a practical usage of the concept of infinity.
A brain with a few billion cells can't comprehend infinity.

>People pretend to comprehend infinity but no one can.
>en.wikipedia.org/wiki/Set_theory
>en.wikipedia.org/wiki/Cardinal_number
>en.wikipedia.org/wiki/Ordinal_number
>en.wikipedia.org/wiki/Surreal_number

>Name me one example of a practical usage of the concept of infinity.
anything involving limits

>Name me one example of a practical usage of the concept of infinity.
>en.wikipedia.org/wiki/Limit_(mathematics)
>Foundation of caculus and analysis

>A brain with a few billion cells can't comprehend infinity.
Holy shit, you're even dumber than I thought.

There are ~100 billion neurons in the human brain. Are you claiming mathematics can't be done with numbers greater than 100 billion, you fucking retard?

All of those reside completely in theory and have no practical value. Those don't apply to the physical world.
>There are ~100 billion neurons in the human brain. Are you claiming mathematics can't be done with numbers greater than 100 billion, you fucking retard?
The human mind can't truly comprehend any numbers above 100

>calculus
>no practical value

>The human mind can't truly comprehend any numbers above 100
>said unironically

>humans- who are finite beings- can't ever comprehend it.
What kind of retarded logic is that?
>humans- who are carbon based beings- can't even comprehend silicon
>humans- who are meat based beings- can't even comprehend plants
>humans- who are bipedal based beings- can't even comprehend wheels
>People pretend to comprehend infinity but no one can.
You don't comprehend what comprehension is.
primes = sieve [2..]
where sieve (p:xs) =
p : sieve [x | x

>The human mind can't truly comprehend any numbers above 100
We are reaching levels of retardation that shouldn't be possible.

>We are reaching levels of retardation that shouldn't be possible.
So > Level 100?

>The human mind can't truly comprehend any numbers above 100
lmfao, you can't count to 101?

You only think you counted to 101, your mind skips one of the numbers to make it work without you consciously noticing, usually somewhere around the 80-90 range.

>lmfao, you can't count to 101?
I can count to it but then I forget the numbers I counted before it as I'm going along- finite memory.

Just think about it, if I try to picture roughly 100 fajitas, for example, I can, but if I go over that it goes all fuzzy and they disappear.

>You only think you counted to 101, your mind skips one of the numbers to make it work without you consciously noticing, usually somewhere around the 80-90 range.
Simple question: What is 100 + 100?

200, obviously. But I didn't do the sum in my head. I did 2+2 and just added in the zero's

You're claiming we can't do mathematics and prove stuff about quantities that are larger than what we can immediately visualize.

So pretty much all of science, physics, chemistry, and biology is useless. OK.

Can you not conceive of a situation where it is useful to deal with quantities >100?

If so, you're autistic.

If you could easily visualize everything expressible via mathematics there would be no point in having mathematics.

Yeah I can see the use, that's where maths comes in I guess. But infinity is different. Not only can't we comprehend it, but it doesn't exist in the finite world of matter we inhabit. Nothing can be done with infinity. It's not just that we can't visualise it, we can't conceive of it at all. We can use maths to conceive of massive numbers, but not infinity, which is a vacuous and nonsensical concept.

Let me guess: You're still doing arithmetic and haven't started calculus?

>infinity, which is a vacuous and nonsensical concept.
Stop.

>what is a limit

It's a load of bullshit that doesn't apply to reality is what it is

>apply to reality

>what is a derivative

lol ok

finitism triggers math autists because it reminds them that their entire field is based on arbitrary axioms that have unintuitive and nonsensical conclusions as a result

Its true i just tried counting to 100 but for some reason i counted 86, 87, 88, 89, 80, which made me go like woah. Took a second to say "90" then start counting again.

Calm down Xavier.

fucking read a book on the hyper reals in in the
pin kys

It's way more autistic to feel the need to introduce a bunch of new axioms just to reinvent the mathematics we already have in a way that doesn't use an idea you dislike.

[math]0.\bar{9}[/math] is a hyperreal

No, it's not. Not in the standard notation.

>what is the last 100 years of physics

Its afflicted with the same problem as the infitesimal though. If one is, so must also the other.
You might be beginning to realize how retarded math is and how much needs to change to produce real results.

Either all of mathematics is wrong because a bunch of brainless retards on Veeky Forums "proved it".

Or the brainless retards are just brainless retards that get triggered when they come across stuff they don't understand properly/don't like.

Sorry but I am siding with my boys Tao, Gauss, Erdos, Hardy, Fermat, Lagrange, Einstein, Euler, Galois, Abel, Russel, Godel, Klein, etc. and not the NJ Wildberger + retarded fags team.

ad hominem, you have no proof and anything you can put forth is just an unfalsifiable theory