How to find an octahedron
I was working on my last Abstract Algebra homework problem: "In how many ways can you color the faces of an octahedron with n colors?" Solving the problem required figuring out all the ways you can rotate an octahedron onto itself, which I was having trouble doing in my head. I asked Selene for an octahedron, not expecting her to have one.
JesseRud: do you have an octahedron i can borrow?
AshLykos: you could go to random.org and look at the first 3 bits of a binary result
JesseRud: what does that have to do with anything?
JesseRud: oh
She had a d8 and let me borrow it after I explained why I needed a physical octahedron. I never expected having friends who role-play to come in handy.
Bad abstract algebra jokes
- A carpool is a group of people who commute with each other. Therefore, a carpool is an abelian group.
- If 1=0 in the zero ring, why don't they call it The One Ring instead?
Yes, I came up with them.
Honest prof
The Abstract Algebra homework is due next Friday evening. Jamie wouldn't say exactly when he would pick it up, but he did give us a probability distribution:
Everything is a set
I think I'm taking Zermelo's idea that "everything is a set" too seriously.
I saw a freeway billboard advertising a SUV or small truck, saying "Category of One". But the Pairing Axiom tell us that for any x, the set of x (written {x}) exists.
My family uses the following strategy to light the Hanukkah menorah: light the Shamash, use the Shamash to melt the wax at the bottom of the other candles and light the other candles, use one of the other candles to melt the wax at the bottom of the Shamash, put the Shamash in place. During Set Theory lectures, I always pointed out when the prof implicitly assumed that a set was nonempty in his proofs. I told my family that our strategy would not work on the 0th night of Hanukkah. (Question for any other Jews reading my blog: Is using another Hanukkah candle to melt the wax of the Smamash disallowed?)
I'm going to take Abstract Algebra I next semester at Pomona College. Groups, rings, and fields... this could be dangerous.
