Mathematicians Play “Set”

Analyst: Set!
Everybody: Where?
Analyst: How should I know? I have an existence proof. It’s not constructive.

Topologist: Set!
Everybody: That’s not a set. You have two diamonds and a squiggle.
Topologist: I don’t get what you’re saying.
Everybody: See? The shapes have to be all the same, or all different.
Topologist: Like… different genus?
Everybody: No, see, that’s a diamond. That’s a diamond. That’s a squiggle.
Topologist: Your mouth is making sounds but none of them seem to mean anything.

Category Theorist: Set!
Everybody: Where?
Category Theorist: See, here’s a set that fails because of the textures. Here’s a set that fails because of the colors. Here’s a set that fails because of the numbers. And all three of them fail because of the shapes.
Everybody: That’s just a bunch of failed sets.
Category Theorist: Only if you look at the wrong level of abstraction.

Probability Theorist: Set!
Everybody: Wait, what?
Probability Theorist: The expected number of sets is almost three. The probability of at least one is nearly 0.97.
Everybody: But we haven’t dealt the cards yet.
Probability Theorist: Exactly. Once you sample from the distribution, all bets are off.

Logician: Set!
Everybody: Where?
Logician: It’s the set of all sets that don’t contain themselves.
Everybody: That’s literally all sets in this game. None of them contain themselves.
Logician: Perfect! Then give me all the cards.
Everybody: “All the cards” isn’t a set.
Logician: Hey, I understand the temptation to define “set” narrowly, but I worry this axiomatization isn’t going to get you anywhere.

Data Scientist: Set!
Everybody: Where?
Data Scientist: Two solid squiggles in each color.
Everybody: Um, none of those cards are showing.
Data Scientist: Okay, the underlying data may have some issues, but my analysis is still sound.

Set Theorist: Set!
Everybody: Okay, before you say anything, is it the empt—
Set Theorist: It’s the empty set!