[todd8]

Perhaps this is true for some texts, but take a look at math journals where mathematicians are writing for other mathematicians within their own field. They reuse symbols, sometime an integral symbol is for Riemann integration and sometimes it's for Lebesgue integration. The subject of the paper will make it clear which is which.

Even in our own field, Computer Science, there are too many confusing cases: Knuth uses |S| to mean the cardinality of set S, |f| to be the number of solutions when f is a boolean, |x| to be the absolute value of x, |z| to be the absolute value of a complex number, and |a| to be the length of a. All within the same book, TAOCP vol 4A Part 1.

[jlokier]

Those notations are well-known standard notation for the same general concept, "the size of".

What "the size of" means is different applied to each type of object, and may have to be defined to explain some of them (esp. |f|), but it's common in math that general concepts apply differently to different things, while having some properties in common.

I think the notation is helpful rather than confusing because "the size of" carries with it some intuitive connotations which are common to each of those examples.