Finitism

[Anonymous No.6627467]

So what do you folks think of finitist mathematics? Do infinite sets really exist or are they just a notational sleight of hand? What would evidence of the existence of the infinite even look like?

[Anonymous No.6627469]

What do you mean by "exist" when referring to an abstract concept?

[Anonymous No.6627471]

>>6627467
finite maths is also just notation, and some rules of manipulation of that notation.

[Anonymous No.6627472]

>>6627469
this.

In combination with real life examples, the symbolic description of finite combinatorics is accessible to anyone who tries - and that's about the only difference.

[Anonymous No.6627480]

>more moldy cheeseburger philosophy spam
Will the shillbots ever get bored?

[Anonymous No.6627484]

Existence is the property that an equilateral triangle with rational coordinates or a fraction in reduced for that squares to two lacks.

[Anonymous No.6627485]

From a 'natural' point of view, the continuum doesn't really fit anything we can observe. We can produce equations which are more easily solved using infinitesimals and infinities, but they aren't necessary for measuring or predicting.
Like complex numbers, they're a tool. There's mathematicians who think numbers altogether are a confusing abstraction that distracts us from the meaning of mathematics.

[Anonymous No.6627489]

He's a crank. Now gtfo.

[Anonymous No.6627507]

>>6627489
Wildberger isn't the only finitist, plenty of mathematicians have been some kind of finitist: Brouwer, Kronecker, Zeilberger, Volpin. This isn't TimeCube, its a serious minority position in mathematics.

[Anonymous No.6627529]

>>6627485
>the continuum doesn't fit anything you can observe
Look around you dumbass. Literally everything in the room you are in including the air is a continuum

>but muh atoms and discreteness
The continuum is an APPROXIMATE MODEL for solid objects and fluids that works extremely well, so well infact that for thousands of years most human beings were convinced everything was continuous

[Anonymous No.6627533]

Oh look, another Wildsperger thread.

[Anonymous No.6627538]

>>6627533
Honestly these threads are alright arguing with Finitists is more fun and interesting than IQ/hw/rank majors/AI whatever else is on /sci/ right now

[Anonymous No.6627548]

>>6627529
But is the continuum best modeled by the (inherently infinite) real numbers or the much more modest rational numbers?
Especially given that no measurement we make could produce something that was unambiguously real rather than rational.

[Anonymous No.6627562]

Infinite math exists. It's possible to do it, most mathematicians use infinity on a daily basis.

If you want to restrict yourself to finite sets 100% of the time, that's fine. I wouldn't expect these people to do interesting work though.

[Anonymous No.6627599]

If you are not okay at least with potential infinities...I don't know, there's not much math left. By potential infinity I mean the idea that you can not exhibit a last element.

[Anonymous No.6627622]

>>6627562
>>6627599
The guys associated with the program
http://en.wikipedia.org/wiki/Reverse_mathematics
have worked those things out. In particular it's not possible to have a "satisfying theory" about even just finite combinatorics, if you disregard infinite sets.
It's worth reading "#0. Introduction." here:

https://groups.google.com/forum/#!original/sci.math/KQ4Weqk4TmE/LE_Wfsk00H4J

But, disturbingly, computability theory has rekt the math of even small concepts no matter how strong your tools. From an MO thread:
>...consider the expressions obtainable by addition, subtraction, multiplication, and composition from the initial functions log(2), \pi, exp(x), sin(x), and |x|. Richardson proved that there is no algorithm to (always) decide whether such an expression defines the zero function.

http://www.jstor.org/discover/10.2307/2271358?uid=3737864&uid=2&uid=4&sid=21104424034313

This implies that I can cook up two mean functions f(x) and g(x), and write down a nice one-liner:
>hey bra, is f(x)=g(x)?
You have no chance to answer it.

[Anonymous No.6627653]

>>6627622
Why is that disturbing? Diophantine equations can't even be solved. Of course transcendental functions over the reals are going to be just as complicated as polynomials over the integers.

[Anonymous No.6627664]

I've done research in infinity sets. Four theorems have been discovered in my work. They are of two types: additive and algebraic. The first two have applications in numerical analysis, and the second two have effect on abstract algebra. Consider the following:

A = {Infinity Set No. 1}

B = {1}

Now,

A + B = {(Infinity Set No. 1) + 1}

Ergo, it has been shown that infinity sets don't contain all sets of numbers, rather only the real numbers.

[Medical_Physicist !!ST92PtcX00D No.6627677]

>>6627467

Mathematical objects do not exist, they are categorized and precise tools coupled with axioms used to make logically consistent conclusions about them.

Even the most basic mathematical idea, a number, doesn't exist. You can show me six apples no problem, but you can't show me a six in and of itself. This is the reason I don't get the qualms over complex numbers people seem to have.

[Anonymous No.6627679]

>>6627653
You're probably right. In any case, it was surprising to me to learn that these simple constituents already let you construct something undecidable.

[Anonymous No.6627820]

>>6627677
They probably are completely aware of this. They just don't like the axioms we choose to to do some math.
I think it's fair enough, although I don't see it as a real problem.

[Anonymous No.6627894]

Arguements between finite and infinite mathematics really tend to boil down to the crossroads of the the mathematical origins of logic, and rhetoric.

Like anything else in mathematics, it's an expression.

[Anonymous No.6628004]

>>6627679
Yeah, it's a nice statement in some ways, compared to Gödel's incompleteness or the word problem for groups or the halting problem, since it's a very concrete example of undecidability that you can tell anyone who knows trig.

>>6627664
What? This sounds like crankery