/sci/ - Science & Math

>>10184553
>>10184527

>>8932114
>So mathematicians find mathematics beautiful, how surprising! You're very stupid.
There are beautiful proofs/constructions/definitions just as there are ugly counterparts to those.

>I am formally trained in mathematics.
>I think GEB is mathematically beautiful.
Choose one, retard.

>popular = beautiful, disregard the fact that GEB is a meme

>theoretical math
Kek, applied math/sciencefag detected. If I would have known that from the start I would have never bothered talking to you as you clearly don't understand real math either. Go masturbate to GEB some more, retard.

>>8518181
>>8518185
>>8518188
>If someone told me I was chatting to a girl in high school, I'd actually believe them

I think what has happened isn't that the AI has become smart enough to pass the Turing test but that OP has become dumb enough to fail it.

>>8219967
>Lemma: If there exists a finite number of objects and they have a total order define on them then there must be a maximum object.

>Given this collection of objects, we can argue that they are not finite. First suppose for the sake of contradiction that the collection is finite, then by lemma we have a maximum object, however using this dumb argument we can always find a more maximum object in the collection therefore our assumption was false and it must not be finite.

You are right in assuming that the axiom of choice is closely related to the concept of infinity on sets. In particular, without the axiom of choice you have many different definitions of infinite set (I saw a paper some time ago that detailed proofs for 8 different definitions, none equivalent to any other).

So, here are some better questions. Even if you prove that the set of integers is not infinite. Then is that sufficient to prove that it is infinite? If so, why? Furthermore, which definition(s) of infinite does it satisfy without having to fall back on the axiom of choice?

>>8161108
>just saying genetic clustering analysis arent always accurate
>The science disagrees, that must mean that the science is inaccurate and our feelings and opinions are correct!!

>>7581577
>All rainforests are the same.
>Just because there exist other things that don't need X it means that all things don't need X.

>>6766244

lol are those economics terms?