1. Let A be an inductive subset of R. Prove that {1} ? {x + 1 |x ? A} is inductive.
2. (a) Let n ? N(Natural number) and suppose that k 2 < n< (k + 1)2 for some k ? N. Prove that n does not have a squareroot in N.
(b) Let c ? R {0}. Prove that if c has a square root in Z,then c has a square root in N.
(c) Prove that 2 does not have a square root in Z.
# Can you someone please help me with these questions.
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