Two Mathy Conversations

These were both fun. The first one was between me and Ed, after advanced calculus one night. We had discussed in class the fact that infinite sums are neither commutative nor associative, e.g., if you start with

1 - 1 + 1 - 1 + 1 - 1 + ....

then

(1-1) + (1-1) + (1-1) + ... = 0

but

1 - (1-1) - (1-1) - (1-1) + ... = 1

even though those are the same terms just grouped differently. Spooky! So here was the conversation.

Ed: The stuff about series was cool.
Me: They're not associative or commutative. It's awful.
Ed: It was neat.
Me: It's wrong.
Ed: It's cool.
Me: It's an abomination.
Ed: I liked it.
Me: It's a sign from God that we aren't meant to do infinite sums.
Ed: It's a sign from God that we shouldn't confuse infinite sums with addition.

The second conversation was last night right after class, between me, another student I'm friends with (Jason), and (at the end) our professor.

Jason: I'm tired of real analysis. I want to do fake analysis.
Me: You could try rational analysis.
Jason: I want to do irrational analysis!
Me: If you're going to do irrationals, you might as well do reals.
Jason: But I'm more the irrational type.
Me: But at least the rationals are a field.
Jason: Then can I do complex analysis?
Me: That's a real course, you know. You can take that.
Jason: It is?
Me: Yeah. They have it here.
Professor: Complex analysis, it turns out, is like Disney World, in that, everything you ever dreamed might be true, turns out to be true.