Let me define two sets:
A={1}
B={1,1}
Few questions:
1. Is A=B?
2. How many elements (or cardinality) does A have? What about B?
3. Is there any time in mathematics that we need to make a distinction between A and B?
(I guess I am just confused, so any guidance would be welcome)
Thanks,
A set is complelety defined by its elements, and since same name means same object (I guess it is quite reasonnable in mathematics): in there is only one thing, which is thus .
When you want to consider a collection of objects and be able to see them appear multiple times, you can use families or sequences or tuples.
EDIT: Ah Tonio was faster
Yes, in multisets: Multiset - Wikipedia, the free encyclopedia, but I have never really worked explicitly with them.3. Is there any time in mathematics that we need to make a distinction between A and B?