Wednesday, April 11, 2007

A neat analysis problem

I'm in thesis-writing crunch-mode, and though there's lots I could blog about, I simply don't have time. Take a look at this problem posted by Guy Gur-Ari, a student at the Hebrew University in Jerusalem:
Let f:[0,1]->R be a real function such that f has a limit at each point.
Does f have at least one continuity point?
It's definitely a good one to work out (try it before you go to his blog for the solution), and check out the rest of his blog while you're at it!

Update: on the topic of analysis, I ordered and am skimming Counterexamples in Analysis -- a must-read for any student of mathematics, though to my relief I seem to already be familiar with most of these. Here's a good one: give an example of a nonconstant function f:R->R that is periodic but has no smallest period. Anyone?

3 comments:

Kenny said...

I never thought about a periodic function with no smallest period, but assuming periodic just means there is a p such that for all x f(x+p)=f(x), then another standard counterexample serves. Very cute!

prof said...

hello
rendez vous sur jewisheritage
a bientot

Leo said...

Shamefully, I don't read French. But if this is an invitation to contribute my own biography as a famous Jewish mathematician, then I'm flattered! :)