1. Let A be an inductive subset of R. Prove that {1} ∪ {x + 1...

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 square root 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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Expert Solution

Colby Messinger answered 2 years ago

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