(adsbygoogle = window.adsbygoogle || []).push({}); The problem statement, all variables and given/known data

Let a > 1 and let S = {a, a^{2}, a^{3}, ...}. Prove that S is not bounded from above.

Relevant theorems

The least upper bound property of the reals and these consequences:

(1) For any real x there is an integer n satisfying n > x .

(2) For any positive real x there is a positive integer n satisfying 1/n < x.

(3) For any real x there is an integer n satisfying n ≤ x < n + 1.

(4) For any real x and positive integer N, there is an integer n satisfying n/N ≤ x < (n+1)/N.

(5) For any real x and e, there is a rational r satisfying |x - r| < e.

The attempt at a solution

I was thinking of a proof by contradiction by I can't think of anything contradictory. Any tips?

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Set of Powers Unbound from Above

**Physics Forums | Science Articles, Homework Help, Discussion**