Yesterday I posed the following problem: If $S$ is the set of positive integers whose decimal expansion does not contain a 3, does

\[ \sum_{n\in S}\frac{1}{n} \]

converge or diverge? My solution is after the break.

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Yesterday I posed the following problem: If $S$ is the set of positive integers whose decimal expansion does not contain a 3, does

\[ \sum_{n\in S}\frac{1}{n} \]

converge or diverge? My solution is after the break.

Here’s a quick math problem to think about. Let $S$ be the set of positive integers which do not contain a 3 when written in decimal. Does the sum of the reciprocals of the numbers in $S$ converge or diverge? I’ll post my answer in the next day or two.

So I took the plunge and decided to start up a blog, primarily as a way practising writing, something I’ve always enjoyed but never made a habit out of. I read a fair number of blogs, but to be honest I wouldn’t miss most of them if they shut down. I’ve found a few which consistently produce high-quality content; here are three of my favourites:

- Paul Graham – A fantastic collection of essays. I like Graham’s writing style more than anyone else I’ve ever read, and don’t understand why the clear, matter-of-fact style that he employs isn’t very commonly used. Many of his essays are about entrepreneurship, which I am not especially interested in, yet I still find his writing engaging.
- Scott Adams – Best known as the creator of Dilbert, his blog is a constant source of unique ideas. As a compulsive thinker who loves kicking around new ideas I look forward to reading his near-daily posts.
- Eric Raymond – An open-source software advocate with an extremely strong ego. The unusual part about that is he actually has the accomplishments to back it up. He writes about a diverse number of things, and his writing is usually interesting even when I don’t care much about the topic.

My intention when starting this blog was to only write about things of interest to me. I had thought that this would necessitate being boring to everyone except in the case where a common interest is shared. Judging from the above list, in the optimal case that’s not actually true.