# The Universe of Discourse

Wed, 14 Jun 2006

Worst mathematical notation ever
All my blog posts lately seem to be turning into enormous meandering rants, which isn't so bad in itself, but I never finish any of them. So I thought I'd just cut this one short and stick to one point instead of seventeen. But someday you're all going to have to read the full article, which complains about how 1960s computer scientists, math grad students, and other insecure people who hunger for legitimacy sometimes try to get it by doing everything with as much notation and pseudo-formal language as possible.

I was reading some lecture notes today, and I encountered what I think must be the single worst line of mathematical notation I have ever seen. Here it is:

$$\equiv_{i_0+1} = \equiv_{i_0} = \equiv$$

Isn't that just astonishing?

The explanation is that the author is constructing a sequence of equivalence relations, each one ≡n derived from the previous one ≡n-1. Eventually (after i0 iterations of the procedure), the construction has nothing left to do, and the new relation is the same as the one from which it was constructed. At this point the constructed relation turns out to be a certain one ≡ with desirable properties.