1. Prove by induction:
(a)
(b) either or ; and
(c) there is no element of in the range
2. Prove by induction on that such that
Also prove that for every , there is an such that .
You can prove some of these without induction, if that is okay with you.
Like Problem 1(c), you can do it by definition of what it means being a natural number.
You can prove some of these without induction, if that is okay with you.
Like Problem 1(c), you can do it by definition of what it means being a natural number.
No. The question specifies to prove the statements by induction. I think the proof relies on the four axioms that a field must satisfy. This is from my advanced calculus textbook (first chapter & first section, btw).