Let S and T be mathematical sets. Now consider the following two propositions:
1. S is a proper subset of T.
2. S and T have the same number of elements.
Are (1) and (2) consistent? That is, can they both be true? If yes, explain how.
If you think (1) and (2) are consistent, then consider whether there is anything to the following analogy. If there is, explain the analogy. There is a set G. G has three disjoint proper subsets, F, S, H. All four sets agree in cardinality: they have the same number of elements.