What are a few of these things people misinterpret? Or maybe even a step back, what's the difference between classical and constructive math?

Well, okay, so the first one is what is constructive mathematics? And people say, well, constructive mathematics is mathematics without excluded middle.

And then this is the first division point where you say, okay, so you mean denial of excluded middle.

And that's most definitely not what I mean.

A lot of what is going on can be compared to a similar situation, say in algebra, where you generalize the structure.

So imagine you have something like, suppose you study commutative groups.

So groups with one operation, an inverse, and the operation is commutative.

Can we maybe step a bit back and make sure that everybody knows what Axiom of Choice is? I think that's the usual story, right? If you have infinitely many drawers and each of them contains a pair of socks, can you select a sock from every drawer?