That would be true, except draws exist

Let's play tic-tac-toe?

All other outcomes are a collaborative aesthetic exploration of a game tree subject to a variety of constraints.

The joy of the game, and indeed the value of the game, does not consist simply of winning. Even in go.

I have a friend who had the license plate "ALEPH NUL" which I thought was good nerd humor.

Tic-tac-toe always ends in a draw with perfect play.

assuming a draw condition is impossible maybe

For a finite game with no draws you are indeed able to.

I am behind the times on some abbreviations. And dense.

What is AD in this context?

Then it's not empty. If it were a union of empty sets, that would be empty.

Another comment in the thread says that “isn't pro-choice” is exactly about the rejection of the axiom.

For anyone wondering what this is

Bertrand Russell coined an analogy: for any (even infinite) collection of pairs of shoes, one can pick out the left shoe from each pair to obtain an appropriate collection (i.e. set) of shoes; this makes it possible to define a choice function directly.

For an infinite collection of pairs of socks (assumed to have no distinguishing features such as being a left sock rather than a right sock), there is no obvious way to make a function that forms a set out of selecting one sock from each pair without invoking the axiom of choice

So mathematicians always make the assumption that they can make a set from an infinite list of other non-empty sets based on this hunch, rather than any concrete choice function. And then they build mansions on top of this foundation, and use it to score chicks and ferraris, smh

... That's the joke. (That he doesn't)