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1. ### Would someone mind checking my proof? Intro Real Analysis

LOL! Thanks for checking XD
2. ### Would someone mind checking my proof? Intro Real Analysis

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!
3. ### Need help on a proof from Spivak's Calculus

I think I took to many steps in the wrong direction. I just kept reducing. I see how you got what you did, I'm going to reassess.
4. ### Need help on a proof from Spivak's Calculus

I started with \sqrt{ab} \leq \frac{a+b}{2} and just went from there like you said in your original message.
5. ### Need help on a proof from Spivak's Calculus

This is a skill I have been learning very slowly, but surely. It's been especially useful for some set theory proofs I've done recently.
6. ### Need help on a proof from Spivak's Calculus

When I did that, I ended up with the statement 2 \leq a+b , which must be true given what's stated in the problem.
7. ### Need help on a proof from Spivak's Calculus

Thanks for the hint. It helped a bit.
8. ### Need help on a proof from Spivak's Calculus

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...