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PorcelainSatan · 18-21, F
It’s convenient for keeping math clean, but honestly, it feels like cheating to just pick from an infinite set without a rule.
Luke73 · 26-30, M
@PorcelainSatan The rule is the choice function XD

DrWatson · 70-79, M
I think mathematics is more cool with it than without it.

For example, we need it to construct the Vitali set, a set which is not Lebesgue measurable.
GoFish ·
never heard of it
GoFish ·
@Luke73 in theory i guess but for what?
Luke73 · 26-30, M
@GoFish That the axiom of choice. And it’s an axiom which means you can’t prove you can. But the axiom of choice and in general sets, are fundamental for mathematics.
GoFish ·
@Luke73 hmm
ElRengo · 70-79, M
Not sure.
The problem resides in the verb to choose
Not easy to select only one element when are continuos and not cleary countable.
Godel...........
Luke73 · 26-30, M
@ElRengo And all the equivalent statements that are obviously true or obviously false.
ElRengo · 70-79, M
@Luke73
There are some statments that are frequently called "trivial" (jargon)
But no statement can be enough defined as obviously true / false
The problem is still the choice.
I wouldn´t say that is always imposible.
But to choose haves some of the nature of to prove.
With Godel in the way........

 
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