Here is my solution. I used mathjax to type it up in Overleaf. I feel like it makes sense, but I also have a feeling I might have "jumped the gun" with my logic. If it is correct, I would appreciate feedback on how to improve it. Thanks!
Homework Statement
I'm currently working through Spivak independently and have reached the problems at the end of ch. 1.
The problem is:
Prove that if 0 < a < b , then a < \sqrt{ab} < \frac{a+b}{2} < b
Homework Equations
Spivak's properties P1 - P12
The Attempt at a Solution
I was...