Sunday, October 28, 2007

Just procrastination . . . .

No, life's not perfect, even in Germany. Like,
  • I split my time between feeling frustrated, because I'm talking in German; feeling guilty, because I'm talking in English; and feeling lonely, because I'm not talking to anyone. It isn't enough to seriously dampen my spirits, but it is enough to make me grateful for the internet and the friendly people who talk to me through the internet.
  • Work's already plentiful and hard -- though this is of course also a good thing, because it's stimulating. (For you mathematicians, here's a nice problem from my half-finished model theory assignment, due tomorrow: prove that there exist uncountably many linear orderings of a countable set of elements.)
I went out hiking in the Black Forest yesterday with my Canadian exchange-student friend Emily, round Schauinsland, the highest peak. We climbed halfway up, got tired, and wandered back down, feeling decidedly superior to the tourists who were taking the six-minute cable car to the top.

4 comments:

Unknown said...

"there exist uncountably many linear orderings of a countable set of elements"

......wait, WHAT?

Unknown said...

Or do you high-level mathematicians use "countable" = "countably infinite"?

Brog said...
This comment has been removed by the author.
hrmacb said...

Indeed, sorry for the confusion.
"dein, cum milia multa fecerimus,
conturbabimus illa, ne sciamus . . . ." --
still countable :)

I realised after chatting to Bojan that this problem isn't quite all it should be; I'd mistranslated out of model-theory-language. Properly, it should be,

"prove that there exist uncountably many linear orderings of a countable set of elements, where two orderings identical up to an automorphism of the underlying set are counted as the same,"

which is somewhat harder (unless you'd assumed this meaning the first time anyway).