Hi! How do you read this theory in English, mainly GenAm/RP?
Theorem one point two.
If an operation consists of k steps, of which the first can be done in n-subscript-one ways, for each of these the second step can be done in n-subscript-two ways, for each of the first two the third step can be done in n-subscript-three ways, and so forth, then the whole operation can be done in n-subscript-one times n-subscript-two ellipsis times n-subscript-k ways.
Is "$\ldots$" informally called "all the way down to" and formally "and so forth"?
In the second case, like "r = 0,1,2,...,n".
How is this sentance said?
r equals zero, one, two, and so on to n.
r equals zero, one, two, and so forth to n.
r equals zero, one, two, and so on n equals n.
r equals zero, one, two, and so forth n equals n.
Are they correct?
What is your familiar way to say them?
Reading mathematical text is not about learning/training english, correctness according to any ruleset should not be a priority. As long as whoever is (supposed to be) listening understands you (and judging from the comments, that's you), you should be fine.
I think what I've heard is mostly "dot, dot, dot". I've never considered that there should be formal as well as informal versions, and I don't think it makes much sense to have such a distinction "$\ldots$" is informal either way.
English isn't my first language either, so adjust your valuation of this answer accordingly.