Do repeated prime factors count as distinct members in a set for proof purposes?

[Zeth]

This is for a proof but I was generally more curious so it isn't in the homework section.

If I were to make a set A which is defined as all the prime factors of an integer a there could be some numbers in A which are repeated, would these count as distinct members or not? The reason why I was wondering is if I made another set by the same criteria for an integer b would and then I made another set C with members A cap B would the repeated numbers show up only as many times as they appear in the set that contains them least or most? I think it should be least but I don't have text on the subject yet and we haven't covered much set theory. I would also appreciate some link or recommendation for a text at 1st year university level.

 

[fopc]

A way to approach the problem is to consider the concept of multiset. Here's a link that should help.

http://en.wikipedia.org/wiki/Multiset

 

[Zeth]

Thanks a lot, that has just the properties I needed for the proof.