Formally speaking the set cannot be constructed using the rules of set theory. So technically speaking it is not a set.
(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?