How to correctly spell some elementary set notations

Question

It may seem a very ridiculous question to you, but its a major problem in many universities around the world when it comes to correctly spell some mathematical notations. Here I want to ask you guys about the correct English spelling of some notations in the set theory and if you can point me to some references that may help me correctly spell mathematical notations.

i.e: Consider $N$ is a set and I want to name some of its subsets and use following notation for my namings:

1. $N_\alpha \subset N$
2. $N^v_\alpha \subseteq N$
3. $N^v\subset N$

What is the correct spelling for above notations? Is it like "N underscore alpha" or simple "N alpha"? For the last two ones, I have no idea how to spell it.

Also, second question is that if it is a good idea to name subsets of a set like this or such notation means more than just naming. In other word, when to use $N_x$ instead of $N^x$.

Answer 1

I assume by "spell" you mean "say out loud".

1 would be "$N$ sub alpha".

2 might be "$N$ to the nu", except that it's not a power. "$N$ sup nu" would do.

3 combine 1 and 3 "$N$ sub alpha sup nu".

I think the power notation is not a good idea. You could use a double subscript $N_{\alpha, \nu}$, read "$N$ sub alpha nu"