What is "$\ldots$" called in English when it comes to counting rule for compound events?

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?

• It is also sometimes pronounced "dot, dot, dot". I don't know whether there is a single, official, conventional, formal pronounciation and / or name. Why would you need one? Isn't it enough that whoever your speaking to knows exactly what you're talking about? Do you foresee any problems with the fact that there may be several equally valid ways to pronounce it? Aug 13, 2018 at 5:42
• My first language is not English, Reading aloud properly while I am writing theorems helps me learn better. :) Aug 13, 2018 at 5:50
• I wonder how people pronounce these signs or symbols when reading context in mathematical theorems instead of reading them sepatately. Aug 13, 2018 at 5:53
• If I were talking out loud I would just say "n one, n two to n k ways" or "n one, n two all the way to n k ways" if I wanted additional emphasis. I would be more likely to hear or say "dot dot dot" if it were being written on a board or something at the time. I think your suggestions sound natural and it wouldn't sound any less fluent. Aug 13, 2018 at 6:07
• Although the three dots are an ellipsis, I have never heard anyone read the symbol aloud as "ellipsis". I speak the Texan dialect of GenAm. If reading the phrase aloud I would probably say "n one times n two, etcetera, up to n k" or "n one times n two, and so on, up to n k". For the second example, I would read "r equals zero, one, two, and so on up to n." Although the word "up" is not needed, the phrases sound wrong to me if I don't include it. Aug 13, 2018 at 6:13

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.