The bait and switch on this one really caught me off guard and gave me a great laugh. Good post.
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
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Congrats, the game is now non-finite (you can just keep drawing forever).
Draw goes to the player who moved second?
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For games that allow that, yep
You can’t draw in pictionairy.
🥁🐍
me, playing for a draw:
love that episode
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 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
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.
Ok, i dont understand this level of math, but cant you force a win in a 2 player game of non-infinite moves? Why wouldnt you be able to? Genuinely asking
Tic-tac-toe always ends in a draw with perfect play.
Mmm, i did overlook the, very obvious in hindsight, draw outcome. Thanks
You could design a different game that does though. E.g. A Tic-tac-toe variant but the player who starts looses if they don’t get 3 in a row by the end of the game.
Your point being?
You can force a win in a specific 2 player game of non-infinite moves(if it has no draw condition). But yeah , it doesn’t apply generally to any 2 player game of non-infinite moves. And the converse also doesn’t apply generally.
assuming a draw condition is impossible maybe
For a finite game with no draws you are indeed able to.
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?
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.
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
If you are so pro-choice, you can split your two balls into several pieces and reassemble them into three balls!
If you are so pro-choice, you can draw two parallel lines and they will always intersect at the horizon!
Sure, why just this morning I got me a second car by choosing five sets of points of my old car and rotating them around a bit in my garage. No, you can’t see it, it was uh… a non constructive job. (jk I don’t own a car, or a garage for that matter)
I hope that at least he believes in the Axiom of Choice.
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)
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?
Then it’s not empty. If it were a union of empty sets, that would be empty.
Fucking relatable !
I’m that guy
