>he believes in the axiom of choice

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you just had to post this didnt you

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even a pupper realize axiom of choice is illogical

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>>8917274

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>>8917274
>he thinks that a nonempty set doesn't have a least element

Exactly what is controversial about the AoC other than the Banach-Tarski "paradox" that was proven to not be a paradox?

>the same mathematicians who believe 1+2+3+4+5... = -1/12 pitch a fit about the claim that given infinite shoeboxes with a complete set of shoes you can pick a left shoe out of each box

>>8917358
AC is equivalent with the law of the excluded Middle

>>8917358
>given infinite shoeboxes with a complete set of shoes you can pick a left shoe out of each box
would you be willing to demonstrate this? no cheating, you actually have to do it an infinite amount of times

>>8917310
Are those three Reimann zetas in the corners?

>>8917370
>every zeta is a riemann zeta
fuck off

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>2017
>he doesn't use some sort of constructive type theory

>>8917364
I thought one of the advantages of human thought over computers was that we could interpret spectrums (in the non-members sense) and breaking things down until they can be reduced to binary logic was how we have to make computers "think"...

>>8917376
*Non-meme
Spell check messed it up.

>>8917364
AC can't be proven from LEM
t. Cohen

>>8917366
There's no way to prove it? Like how you can prove a limit without making an infinite chart?

>>8917380
exactly. limits make no sense

>>8917382
le wildberger face

>>8917311
unrelated

>>8917364
no,
in the context of many set theories, AoC implies LEM.
LEM doesn't fucking imply AoC.

>>8917358
It's just a non-constructive existence axiom.
It leads to statements of the form
>the exists (via AoC) an X with property P(X), but we can also proof that we can't provide X in terms of something else. But it "exists"!

>>8917274
AoC is true for a class of finite sets.

Adopting it for bigger sets is just "wishful thinking" and creates a framework of "sets" that feels nice but would but highly non-constructive without AoC.
I see no point to choice, desu., it's just needed for some theorems in functional analysis, and some useless theorems elsewhere.
But it's all non-constructive, so not applicable to anything you can implement on a computer.

I'd say adopt choice, but vastly restrict the size of your sets.

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>>8917274
He doesn't believe in the intermediate value theorem.

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>he believes in square roots

>>8917358
>>8917366
Actually that's possible with this terrible shoes analogy, you can discriminate elements (right shoes/left shoes) in the boxes so you can say "I pick the right shoes of every box", this is a ZF valid choice function.
If it was socks, then you can't because there is no way to discriminate the socks, you can only say "I pick one of them in every box", wich need AoC to be a valide choice function.