Question 5. (3 points) A natural number n is called even f there is a natural...

Transcribed Image Text:

Question 5. (3 points) A natural number n is called even f there is a natural number m such that n = m + m, and odd, if there is no such m. Prove that every natural number is either even or odd, and moreover that if n is even, then S(n)= n + 1 is odd, and vice versa if n is odd, then S(n) is even. You may use the fact that N is closed under addition and multiplication in R, as well as the Peano Axioms (with S(n) = n + 1), and all other results we proved about natural numbers, or the properties of a field. Question 5. (3 points) A natural number n is called even f there is a natural number m such that n = m + m, and odd, if there is no such m. Prove that every natural number is either even or odd, and moreover that if n is even, then S(n)= n + 1 is odd, and vice versa if n is odd, then S(n) is even. You may use the fact that N is closed under addition and multiplication in R, as well as the Peano Axioms (with S(n) = n + 1), and all other results we proved about natural numbers, or the properties of a field.

Answer rating: 100% (QA)

The natural no can be found as illustrated and exp... View the full answer