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Peter Johnstone taught me that 0 was {}, 1 was {{}}, 2 was {{},{{}}} and so on. But what about all the people who didn't go to that class?
Set theory is *one way of doing mathematics*.
Type theory is *another way of doing mathematics*
In mathematics, when you say "let G be a group" what you mean is that G is a set, and G has elements, and the elements are all individual "atoms", and that it is impossible to split the atom.