Question

Consider the three restrictions (i), (ii), and (iii) placed on the sets in Cantor’s Theorem. (a) Find a sequence of sets that satisfies (i) and (ii), but . (b) Find a sequence of sets that satisfies (i) and (iii), but . (c) Find a sequence of sets that satisfies (ii) and (iii), but .

Answer 1

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Explanation:

When it comes to the field of elementary set theory, Cantor's theorem is a basic result which affirms that, for whichever set, the set of the entire subsets will have a strictly bigger cardinality than itself. For the finite sets, Cantor's theorem can be affirmed to be true by plain enumerating the number that are in the subsets.

The full step by step explanation is in the attached image below