If we consider a set of natural numbers, say 1, 2 and 3, and another set consisting of 1, 2, 3 and 3, why can we say that these two sets are equal?

According to Cantor's idea of a set is that it is a collection of distinct objects, and 3 and 3 in the second set are not distinct but equal, so they must be considered as one. Thus the second set equals the first.

but..

If we visualize the two sets as two balloons, where one ballon has the elements 1, 2, 3 and the other one has exactly the same but one additional 3. Since the second balloon does not consist entirely of distinct objects, can it still be considered as a set? In my understanding, the two 3's can also be considered as two objects, and the two sets don't consist of the same elements, since one has an additional 3.

I know this may sound a bit silly, and I completely understand the argument that we should consider same objects as one and represent them only once in set notation, but it's still interesting to consider this scenario.

Greatly appreciate any input, but please no negative ones.