- #1
Tasaio
- 20
- 0
Hi there,
I'm using Spivak's Calculus. Some of these questions are giving me trouble...
6.(a)
Prove that if 0 <= x < y, then x^n < y^n, n = 1, 2, 3, ...
Suppose 0 <= x < y.
...
Since this is Chapter 1, I shouldn't be using induction. ;-)
I'll try anyway.
Let S be the set of positive integers n for which:
If 0 <= x < y then x^n < y^n
Case: n = 1
Since x < y, then x^(1) = x < y = y^(1)
So 1 in S.
Assume k in S.
Then if 0 <= x < y, then x^k < y^k.
Case: n = k + 1.
Suppose 0 <= x < y.
...
Here, I get stuck.
Does anyone have an idea about what to do next? Also, is there possibly a way to do with question without using induction?
Thanks in advance for any assistance,
Tasaio
I'm using Spivak's Calculus. Some of these questions are giving me trouble...
6.(a)
Prove that if 0 <= x < y, then x^n < y^n, n = 1, 2, 3, ...
Suppose 0 <= x < y.
...
Since this is Chapter 1, I shouldn't be using induction. ;-)
I'll try anyway.
Let S be the set of positive integers n for which:
If 0 <= x < y then x^n < y^n
Case: n = 1
Since x < y, then x^(1) = x < y = y^(1)
So 1 in S.
Assume k in S.
Then if 0 <= x < y, then x^k < y^k.
Case: n = k + 1.
Suppose 0 <= x < y.
...
Here, I get stuck.
Does anyone have an idea about what to do next? Also, is there possibly a way to do with question without using induction?
Thanks in advance for any assistance,
Tasaio