Yesterday was quite a math day. In particular, it was largely a topology day. After classes, I went to Annalies’s house to get half the topology homework done. Then we went over to the Math Department Mailroom for the first meeting of Math Club. The advisor of the math club, Daryl Cooper, gave us three problems to work on. One of them was: Find a positive integer y such that when the leftmost digit of y is deleted and inserted at the right to form x, 2y=x. Unfortunately, he didn’t seem to like my base 100 solutions based on 1/7 (142857 and friends) as much as I did. Anyway, after that, we were a few minutes late for Ben’s topology group. Annoyingly, he seems to think that one can’t state that (A union B)/A is homeomorphic to B/(A intersect B) by complete obviosity. (Yes, I learned what quotient spaces are, and I like them. They’re very friendly.) I need to find a topology book that doesn’t assume that the reader already knows more topology than is in Sutherland, as Hatcher does so that I can start proving that spaces are homeomorphic rather than saying that it’s blatantly obvious (which is usually is). Math days are fun. I need to have more of them.

Today I did just about nothing other than fix typos in my algebra notes. If you’re interested (or if you aren’t), my group theory notes no longer have any Diagram Omitted labels, as I figured out how to make the diagrams and put them in. I need to get some work done on Haar measure. I keep reading the same three pages day after day, and I even understand it. But for some reason, I can’t seem to stop myself from rereading it.

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## About Simon

Hi. I'm Simon Rubinstein-Salzedo. I'm a mathematics postdoc at Dartmouth College. I'm also a musician; I play piano and cello, and I also sometimes compose music and study musicology. I also like to play chess and write calligraphy. This blog is a catalogue of some of my thoughts. I write them down so that I understand them better. But sometimes other people find them interesting as well, so I happily share them with my small corner of the world.

porky

well, *i* like your base 100 solutions =p

Did you discover them by calculation, or by remembering facts about 1/7?

Is there a nice way to see if there are solutions in a given base?

I found that one by remembering facts about 1/7. I don’t know how to determine whether there are solutions for a given base though. You might try looking in

The USSR Olympiad Problem Book.