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

I would say the number in this set, Calli. The number of the set could be a designation, though in my experience sets are designated by letters, not numbers. But it's not impossible to think that you might come across a situation where you would say, for example, that set number one contains five elements and set number two has six elements in it, etcetera.

If you're speaking to people who should know math, use the word 'cardinality.' http://en.wikipedia.org/wiki/Cardinality
"The cardinality of the set A is n."

Or you can say, "The number of elements in A set is n" or very loosely "the size of A is n". It depends on the audience, but probably just saying "the number of elements" would be clear and correct to anyone.

Perhaps: 'The number of elements in this set'
No confusion there.

Can you provide the actual sentence as it is in the wild?

Quantity would apply also.
The Quantity of this set.
The Size of this set.
The Total (count) of this set.

How about; All o da stuff hea'

me?

The whole thing is:

...

...Some formula...

Where K denotes the total number of clusters and m is the sum of all members in cluster i.

...

From the context, I figure out that K and m both mean the size. K means how many clusters and m is the size of a cluster. m is not the sum of all the members of cluster i. The member in cluster i is document.

Any suggestions on what to say about this more clearly?

In this formula K equals the number of file folders, also called clusters; each folder holds a number of documents. We will use M to mean the number of documents that are in any one file folder. We will designate the file folder as i.

And this, Calli, is why we have jargon such as "Where K denotes the total number of clusters and m is the sum of all members in cluster i."

It took me more than twice as many words to get the point across, but that is totally unnecessary if the person reading the article understands the jargon. I spent many years as a writer who specialized in taking jargon and turning it into the language of the common folk, and there is a fine balance between being verbose and not getting the jargon simplified so the common folk can understand it at the first reading.

Ted, your explanation is clear to me.

For here the "set" is a folder, and the member is "document", so the "sum" of all the members can mean nothing but the number of documents in the cluster.

If the case is a general set, which might be a set containing numbers, say 1,2 and 3, "the sum of all the members" then can mean 1+2+3=6, or the total count of all the members, i.e., 1+1+1=3. In this case, should we avoid use the word "sum"?

The complete context makes it clear. Yes. The word "sum" should be avoided in this instance. It should read, perhaps,

"Where K denotes the total number of clusters and m is the number of members in cluster i."

Depending on context, I might eliminate the word "total" above.

Ted, your explanation is clear to me.
Nice cross-thread, calli!