The bait and switch on this one really caught me off guard and gave me a great laugh. Good post.
I hope that at least he believes in the Axiom of Choice.
… That’s the joke. (That he doesn’t)
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
Another comment in the thread says that “isn’t pro-choice” is exactly about the rejection of the axiom.
On the other hand, he Doesn’t think you can double a sphere by cutting it into 5 pieces and reassembling them, so there’s that.
It’s been a while since I’ve done products of sets, but what if one of the sets in the product is a set of empty sets?
Finite games are all definite, either player 1 as a winning strategy or player 2 has, all other “outcomes” are just mental illnesses. Get over it, math doesn’t care about your feelings.
That would be true, except draws exist
Tie goes to winner of the next game, easy fix
Congrats, the game is now non-finite (you can just keep drawing forever).
For games that allow that, yep
You can’t draw in pictionairy.
🥁🐍
I thought I understood sets until I saw a show on PBS where a guy showed how there were different infinities using them and I realized I knew nothing.
I have a friend who had the license plate “ALEPH NUL” which I thought was good nerd humor.
The movie theater in Futurama is called Lowe’s Aleph-Null-Plex.
Nice, I missed that one
Hey now, just because someone isn’t pro-choice doesn’t mean they’re pro-AD. Honestly, people nowadays think everyone who disagrees with them on one thing must have every unhinged belief under the sun.
I am behind the times on some abbreviations. And dense.
What is AD in this context?
If I open up a pack of biscuits, and we each take turns eating a biscuit, AD says that there’s a dominant strategy that can ensure that I eat the last biscuit. (e.g. there’s only 1 biscuit; I win, or there’s an odd number of biscuits; I win)
i.e. AD says you can rig games like this from the start
The axiom of determinacy, which implies some of (or all?) of the statements in op, and is more or less stated at the end. AD implies ~AC but they’re not equivalent.
