/sci/ - Science & Math

>>12541604
Such as?

>>12541608
The real numbers.

>>12541687
oh no it's a wildberger poster

>>12541704
oh no it's an infinitist schizo

i want to huff tomoko's dirty feet

>>12541604
If so it should be easy to derive a contradiction from it which would instantly propel you to mathematical fame

>>12541764
In general it's very very hard to derive contradictions for axiomatic systems.
Take for example how long it took for us to prove FLT. We could have taken something like (not FLT) as an axiom and wouldn't realize our system is contradictory for centuries. This is actually very likely to be the case with our current mathematics.

>>12541604
sheaves/topoi

>>12541604
Sort of. I thought the other day, isn’t rigor still ultimately arbitrary? How can you determine which definitions are sufficient? Even for undefined terms, there’s still necessarily a certain amount of ambiguity involved in language.

>>12541604
choice

>>12542084
If you want to you could formalize something in a proof assistant like Coq.

>>12542113
>a product of non-empty sets can be empty

>R controversy

i dont see the issue with real numbers. they can be infinitely refined depending on computational power. they are as "real" as you need them to be.

root 2 bothers me a little i guess but whats the problem with infinity ?

>>12541604

College algebra is pretty bullshit.

If you don’t pass algebra in high school, or an entrance exam that includes an algebra section, then you shouldn’t get admitted to college.

>>12541604
The only bs proofs are those that prove things that are obviously retarded. In this case, there is only one real example in modern mathematics: the existence of a non-measurable set. But the proof that started this nonsense is the proof that the real numbers can be well-ordered, a "fact" which is obviously false, and which required a long time to clarify, basically until Paul Cohen showed that you can make it false as easily as you make it true, so that it is more correctly false than true (that's not exactly correct, it took several years after Paul Cohen, but the main idea is Cohen's).

The proof that the real numbers can be well-ordered (put into an uncountable ordered list, so that each real number is at one and only one position, and the list has the property that it is discrete and finite when counting down, meaning that every subset has a least element) is as follows:

1. choose an element from every nonempty subset of R.
2. consider the entire set R, you chose an element (it's a nonempty subset of R), so call that the "first" element of R.
3. Now consider R excluding your first element. This is nonempty, so you chose something from it. Let this be the second element.
4. Now consider R exluding the first two elements. This is nonempty, so you chose an element from it. Let this be the third element.

This is an inductive procedure, so it extends to all integers, and then to all ordinals, which are linearly ordered collections which are inductive, like the integers. For the countable ordinals, this is not an intuitive paradox--- you can embed any countable ordinal in R. But when you admit uncountable ordinals, and R as a set, then you can show that there is an ordinal which exhausts R in this way.

The reason is that the union of all the ordinal maps that go into R in this way has to crap out somehow, or else the set R bounds all ordinals. But no set can bound all the ordinals, because then you can define the set of ordinals as a subset of R with certain conditions (and then use replacement to map back to the ordinals). But there is no set of all ordinals, because such a set would be an ordinal, and then taking this ordinal plus 1 would give a contradiction. So the result is that, if R is a set in the usual sense, you must have well ordered it.

This is an obvious lie, ordinals can't map to R in any normal sense, there are no non-measurable sets. This proof, the well ordering of R, is not mathematics, it is theology.

In modern set theories, you know from the Skolem theorem that you might as well work with a countable model, then the theorem is simply showing you that the countably many elements of R in the model map 1-1 to an "uncountable ordinal" (which is countable in the model, just the model doesn't know it). That's the resolution. The other paradoxes where you inductively partition R into dusty collections that violate intuition all basically rely on this enumeration of R into an ordinal list, which works in axiomatizations of set theory only because these axiomatizations are secretly countable, and describe only countably many real numbers in some philosophical sense of minimal models.

The proper perspective is that the real numbers are not well-orderable, and there are no non-measurable sets. This is the property of many modern set theoretic systems, all of which are rejected, because mathfags are too used to choice and powerset. The real problem in the proof is not the choice step, it's the powerset step, assuming R is a set. This is the central mistake, and it is deeply imbedded in modern mathematical practice, no matter what results set theorists come up with. For more about this, look up Solovay model and modern models of the Axiom of Determinacy.

>>12541604
n-th order moments (for n>2)
fractional derivatives
any dimensional/combinatoric math helping further string theory

>>12542354
>root 2 bothers me a little i guess but whats the problem with infinity ?
Those are literally the same problem.
https://www.youtube.com/watch?v=REeaT2mWj6Y