I'm reading a paper authored by a peer, in which there is one line like this:

...the number of this set...

In fact, the author is trying to say how many elements there are in the set.

I doubt whether the term "number" is fit here for it would be ambiguous. It can mean how many elements or the "serial number" of the set. Or it can even also mean the element of the set if some element of the set is a number.

I dwelled on how to reword the snippet. First thing came to my mind is:

...the count of this set...

or

...how many elements in this set..., for example, k denotes how many elements in this set.

Which way would be better? Or Are there other ways I could rephrase the sentence?

Thanks,

Callithump

Do inform me if you see any corrections needed in my written English.