For any set A, define the successor of A, denoted S(A), by S(A) = A ∪ {A}. One way to "construct" the natural numbers and zero from set theory is by the following correspondence:
0 ↔ ∅, 1 ↔ S(∅), 2 ↔ S(S(∅)), 3 ↔ S(S(S(∅))), . . .
Note that the axiom of infinity guarantees that all of these successor sets exist. Show that 5 ↔ {O, 1 , 2, 3, 4 } .
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