Countable Sets with repeated Elements

(System won't let me respond to map (m,n) to N so I will address the issue involving the last reply here. Which is just as well as it's really a separate topic.

Slipstream comment is valid. I did have a reservation about my post based on the following:)

THE QUESTION:

A={a,a,a} and B={a} have the same size (cardinality) based on the fact that they are the same sets. AsubB and BsubA.

Are {a,a,a,a,........} and {a} the same size, ie, countable?

Re: Countable Sets with repeated Elements

Formally speaking the set $\displaystyle \{a,a,a,\dots \}$ cannot be constructed using the rules of set theory. So technically speaking it is not a set.