OK, I don't want you to think Sunok-girl is entirely stupid, she's said quite a few useful things in Number Theory. But those aren't nearly so funny, now are they?
Most of Number Theory today was spent talking about cancellation - when it holds and how we might try to prove it. Immediately, when Glenn put the statement up on the board, I said to Chris, "Some first year is going to say we can prove it by multiplying by 1/a." Chris thought no, by this point they had learned better. Thankfully, when Glenn asked if anyone could prove it, Chris was right.
Anyway, one girl asked how cancellation could possibly be false, and so Glenn gave a counterexample in Z6, namely, 2·1=2·4, and 2≠0, but 1≠4. To this Sunok-girl responded with, "But if you simplify 2·4 into 2 before you divide by 2, you're OK." I don't think I've ever heard a more awful misunderstanding of how math works...
At one point, later, it was mentioned that cancellation holds in Q, and a first-year said he could prove it there, using inverses. And then - just soon after that - ∞-boy says he can prove cancellation in Z the same way! Gah! And he waited till now to say so...?
So yesterday in Geometry, Rosenberg talked about why axiomizing Euclidean geometry is pretty inconvenient (it's nasty), and today, he talked about why he thought the coordinate approach to also be inconvenient - it assumes we understand the real numbers. And, he said, most people really don't.
To demonstrate, he said we would play the UN game. UN as in United Nations. How do you make a United Nations? You take all the countries, and you take one representative from each of them... I think you can see where this is going. So we would divide R into countries, and then take one representative from each of them. So first we divided it by a≡b (a is from the same country as b) iff a-b∈Z, then by a≡b iff a=b, then by a≡b always, and finally, of course, by a≡b iff a-b∈Q.
In the first 3 cases, obviously, we could easily come up with appropriate United Nations, but, you know how this goes, in the fourth we ran into quite a bit of trouble trying to name one. So, he says, maybe there isn't one. Let's take a vote: Who says there is a UN? A bunch of us raise our hands. Who says there is no UN? No hands are raised, but Tan Dan responds, "George Bush".
So the second half of Geometry was all stuff I had already seen last year (well, I had seen the whole slice-of-Q-acting-onR thing before in Geometry too, obviously, but not in that lesson), so I thought to try to list all the elemental symbols I could think of. (There are currently 111.) I managed to get all but 7. While Cameron went and described research labs I wasn't interested in, I came up with 3 more, and one more at dinner; then I showed it to Chris. He came up with the three I was missing - Pa, for protactinium, Sr, for strontium (how did I miss that one?), and Tm, for tamarium. Yay for pointlessness.
Of course, some of you may realize that's not the whole story. I just went and checked an actual periodic table, namely, webelements - Chris had checked against his pocket one earlier, but apparently not very thoroughly - and I saw Tm, but on pointing to it, it said it was thulium. Funny - I had thulium down as Tu. And I can't find a Tu on here... so I got one of my symbols wrong, and Chris made up an element to fill the hole. But this meant I was missing one again... I had missed Bh, for bohrium. Actually, I had thought of that one earlier, but hadn't put it down because I wasn't sure that was its name.
...that's really all for now, unless you want me to retell some of Matt and Eli's stories.
-Sniffnoy
