He believes in the axiom of choice

>he believes in the axiom of choice

you just had to post this didnt you

even a pupper realize axiom of choice is illogical

...

>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

AC is equivalent with the law of the excluded Middle

>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

Are those three Reimann zetas in the corners?

>every zeta is a riemann zeta
fuck off

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

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"...

*Non-meme
Spell check messed it up.

AC can't be proven from LEM
t. Cohen

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

exactly. limits make no sense

le wildberger face

unrelated

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

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"!

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.

He doesn't believe in the intermediate value theorem.

>he believes in square roots

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.