How to say math terms in English

Question

I would like to know how to say in English the following objects:

1. the quotient $\mathbb R / \mathbb Z$ (is it "Ar over zee"? or "Ar modulo zee"?)
2. things like $[0,1]^n$ (is it "the n-th power of the unit interval" or "zero-one to the n"?)

(I am sorry if this question already has an answer here, but I could't find it. Also hope it's the right place to ask.)

Answer 1

As already has been pointed out in the comments above, there will be a slight difference between American English and British English. Also, people have different ways to say the same thing. For the two above, I would personally say

1. The quotient R mod Z (ar mod zee)

2. Here I would say one of the following:

   • the closed interval from 0 to 1 to the n.
   • the unit invertal to the n.

All this depends on the given situation. If I am talking so someone and we are not writing anything down, then I would take care to be precise in how I say thigs. So I might even say: Now lets consider the unit inverval. Take the direct product of this intercal with itself $n$ times.

If I am at a blackboard presenting things, I will often not say everything that I am writing. Here I might end you saying: Let's consider the following direct product. So I might not even say out loud that I am thinking about the uni interval. In these situations it also depends a lot on what is important. If a certain definition is important for what I will say later, then I will make sure to be very careful and I will repeat things differently.