[xchkr1337]

If you open any reasonable math textbook (except for maybe logic related ones), chances are, you won't see the ∀ symbol anywhere at all. It's often considered bad taste to write a symbol like this when you can just write "for all". The main obstacle in learning math comes from not understanding the background material enough and basically never from not understanding the notation.

[skydhash]

And the notation are introduced to you gradually. Even books that do not have a chapter on the notation used, will have a reference page. If not, you’re not reading introductory material and some background is assumed.

[marssaxman]

How would the notation be "introduced to you" at all, when reading source code? What book would there be? How would you know how to find it?

This is a serious drawback to the traditional math notation: if you didn't come up along one specific educational pathway, it seems to be effectively impossible to work your way in and figure out what any of it means. You can't pronounce any of it, you can't look it up; even if you can work out the names of the symbols, they often mean different things in different contexts. It is a mess.

For many years now, the way I have ingested CS papers is to read the introduction closely, getting my head around the concept, then bail out once the inscrutable symbols show up and go find an actual implementation in some real, documented, parseable programming language - any one will do - from which I can readily infer what the rest of the paper was supposed to mean.

[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.