"The paradox: Let T be a standard first-order formulation of ZFC. Assume T has a model. By Skolem's Theorem, T has a countable model M. Since T ⊢ ∃A(A is uncountable), M ⊨ ∃A(A is uncountable). But how can M—i.e. a model that “sees” only countably many things in the universe—“say” some sets contain uncountably many elements? How can M account for all the “extra” members of A? It can’t. According to M, A can be at most countable as there are only countably many “things” available (in the domain of M) to be in A. So A paradoxically looks countable and uncountable." Is there anything WRONG? UNECESSARY? MISSING? Or, is there a simpler way to put it, so that a 10 year old could understand it? Gracias.