/sci/ - Science & Math

>>12448934
>Naturals end at h. they are finite under infinity due to infinite density of numbers.
h being?
>they are finite
by construction they are clearly not
>neighborhood of infinity
oh nevermind you're a memesperg
>is it true that rational over rational is rational
yes, it's a trivial proof due to closure of natural multipliation
>are rationals closed under addition
yes for the same reason

>>12448934
Please read an undergrad analysis textbook.

>>12448945
>h being?
the number in the neighborhood of infinity. I've defined it to have the property 1/0.
pic related should reveal more.
>by construction they are clearly not
then they don't have infinite density and you're using satan's reals.
>oh nevermind you're a memesperg
sorry you can't handle the truth
>yes, it's a trivial proof due to closure of natural multipliation
>yes for the same reason
So then the Operative Algorithm containing 1,2, of some length is rational too?
>>12448951
No.
they use logic, and I hate logic. Sorry I'm not a schizo retard.
intuition > schizophrenia.

>>12448934
Is denying the reals the new 0.9999...=1 now? At least try to be interesting and deny transcendental numbers. I don't think anyone sane enough will start arguing about the truthfulness of the Pythagorean identity.

>>12448998
answer the question goy
>
>yes, it's a trivial proof due to closure of natural multipliation
>yes for the same reason
So then the Operative Algorithm containing 1,2, of some length is rational too?

>>12448998
I can implement natural and rational numbers on a computer, add them, subtract them and do various other operations with them. How do I do the same with your numbers? What would sqrt(2) look like?

>>12449013
cs fag can't comprehend anything he can't put in a computer
>muh everything in math is arrays

>>12448998
you do realize transcendentals are elements of the reals, right?

also, pythag's identity fundamentally assumes geometry is euclidean, which invokes the "parallel lines never meet axiom". but it's well known now that you can drop or replace this axiom and still have interesting math (non-euclidean geometry). it's not as obvious as it seems

>>12449013
>What would sqrt(2) look like?
to be exact you'd have to store it as sqrt(2)

>>12449045
adding to this, properly speaking positional number systems (i.e. decimal), are representations of reals, not the reals themselves

>>12449039
>you do realize transcendentals are elements of the reals, right?
yes, that was the whole point of my post. At least try to be interesting and argue that, unlike algebraic numbers, transcendentals don't actually "exist". Because your shit is just boring middle school level denialism about "hurr durr how can numbers have infinite decimals".

>>12448998
Denying irrational numbers is just a result of your choice of axioms. If you look at common constructions of real numbers (dedekind cuts, cauchy sequences, infinite decimals, infinite repeat fractions, etc.), all of these require some form of infinity (either an infinite set or doing infinite operations) to realize. As a result, it is not far-fetched at all to reject real numbers if you are a finitist.
And at least for your diagram, this is why wildberger (as a prominent example) uses quadrances (the square of length), to describe his concept of length. He would say that diagonal does not have a length. Is it counter-intuitive? Yes, but there are some unintuitive consequences of the axiom of infinity as well (like banach-tarski or some weirdness as a result of the axiom of choice). These are usually brushed off because they are physically unrealizable, but you could say the same thing for your triangle here (you are never going to have two perfectly equal line segments and a hypotenuse that perfectly connects them with no overlap).
0.999... = 1 is completely different. They are trying to dispute a proven fact within R. Rejecting R itself comes from your choice of axioms.

>>12451158
There currently isn't a way of constructing the real numbers in a purely finitistic manner. You can argue that finitist math isn't useful, but you aren't saying that. Please do some research on what you are arguing against, otherwise you will sounds like a middle-schooler yourself. The argument is not "how can numbers have infinite decimals" (tons of rationals have infinite [repeating] decimal expansions).

>>12451528
>There currently isn't a way of constructing the real numbers in a purely finitistic manner.
yes, and? Finitists can suck a fat one then. Denying a useful concept because it does not fit your idea of what "good" math is supposed to be like or whether something "actually exists", whatever the fuck that is supposed to mean, is fucking dumb. The only time a theory doesn't do it is when it contradicts itself. Try to pull your head out of your ass and be a bit more pragmatic.
>Please do some research on what you are arguing against
I've read enough schizo "articles" that try to solve a non-existent problem.

>>12451591
>Finitists can suck a fat one then
Not an argument.

>Denying a useful concept because it does not fit your idea of what "good" math is supposed to be like or whether something "actually exists", whatever the fuck that is supposed to mean, is fucking dumb.
I am not saying you should reject infinitist methods. If you read my previous post, all I said was that it is impossible to construct R with finite methods only. I also never said that this was superior to having infinities.
Other people have different views on what is useful/worth investigating than you and either you can come to terms with that or continue to autistically rage at other people on imageboards.

>Try to pull your head out of your ass and be a bit more pragmatic.
Lmao, mathematicians are the last people who should be advocating pragmatism. For starters, almost all of set theory is a purely logical undertaking. Please pull your head out of your ass and realize that some people are interested in seeing what a non-standard point of view (e.g. rejecting the axiom of infinity), can give us in terms of new mathematical techniques.

>I've read enough schizo "articles" that try to solve a non-existent problem.
Okay, then please try reading non-"schizo" articles and see where that takes you. As an example, rational trigonometry is an alternative way of doing standard trigonometry which is interesting since there is no direct use of transcendental functions. Once again, it is an interesting intellectual endeavor and may offer someone a new way of thinking about things, even though it may have no practical impact on how we traditionally do math.

>>12451653
>Not an argument
yeah, no shit. Me fucking your mom isn't exactly a debate.
>Other people have different views on what is useful/worth investigating than you
they sure can, but they need to justify their efforts with some actual productive results. So far I've seen none.
>For starters, almost all of set theory is a purely logical undertaking.
and how does that invalidate my point about pragmatism? Pragmatism is sticking with things that work and not getting caught up on things that don't. Set theory works so well, that we reformulated all of modern mathematics around it in a single framework. If that ain't useful I don't know what is.
>some people are interested in seeing what a non-standard point of view (e.g. rejecting the axiom of infinity), can give us in terms of new mathematical techniques.
I certainly approve of the endeavor, but it still goes back to my point. This topic is at least a century old and so far nothing useful has come out of it. Name me a single technique that finitists use that gained traction in other areas of math.
>As an example, rational trigonometry is an alternative way of doing standard trigonometry which is interesting since there is no direct use of transcendental functions.
It's a subset of trigonometry. There are many fascinating conclusions you can derive if the ratio between the x and y coordinates is a rational number, but it does not invalidate any of the conclusions from doing geometry with irrational angles. So how is this supposed to convince me that I need finitist reals?

>>12451666
>Me fucking your mom isn't exactly a debate.
Not an argument. You can continue pretending you're being aggressive but it's actually pathetic.

>Pragmatism is sticking with things that work and not getting caught up on things that don't.
Well, math with only rational works, in that there is no logical inconsistencies. It may be less powerful (sqrt(2) is not a rational), but once again, I assert that mathematics is a logical endeavor. Pragmatism should have nothing to do with what someone should investigate. And you are not the arbiter of what is pragmatic and what is not. New points of view are interesting and no one should be stopped from looking at things in a different light.

>Name me a single technique that finitists use that gained traction in other areas of math.
Take a look here: https://math.stackexchange.com/questions/1989695/why-isnt-finitism-nonsense?rq=1
Basically, the crux of the argument is, to the surprise of no one, artificially putting constraints on the way that someone should think limits the ideas that can come out.
And also, even if something never comes out of finitism in your lifetime, why does that bother you? Unless you are somehow being harmed by a finitist's philosophical stance on math, it's their choice and they can approach things however they want. All I'm saying is that it's a valid philosophical position to take on math.

>So how is this supposed to convince me that I need finitist reals?
Once again, I never said you need to drop reals. All I said is that finitism shouldn't be dismissed because it isn't "pragmatic" (nothing should be).