I think I am finally starting to understand the basics of discrete mathematics. Although my first proof, I didn't do so well on, I did pretty good on the test after studying a lot.
Anyways, thanks in advance again guys/gals for all your help. I was hoping you could check this proof that I am doing by mathematical induction. Also, in addition to verifying, my grader is really strict on structure of the proof and explanation, so feel free to make suggestion on how to make this clearer.
Prove that if 0 <=a < b, then a^n < b^n for all positive integers n.
Basis Step: If n=1, then a^1=a < b= b^1
Induction Step: Suppose a^k < b^k.
Then,
a^(k+1)=a (a^k) < b (a^k) < b (b^k)
and b(b^k) = b^(k+1)
Therefore, a^n < b^n for all positive integers.
Thanks again.
Anyways, thanks in advance again guys/gals for all your help. I was hoping you could check this proof that I am doing by mathematical induction. Also, in addition to verifying, my grader is really strict on structure of the proof and explanation, so feel free to make suggestion on how to make this clearer.
Prove that if 0 <=a < b, then a^n < b^n for all positive integers n.
Basis Step: If n=1, then a^1=a < b= b^1
Induction Step: Suppose a^k < b^k.
Then,
a^(k+1)=a (a^k) < b (a^k) < b (b^k)
and b(b^k) = b^(k+1)
Therefore, a^n < b^n for all positive integers.
Thanks again.