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  1. CaptainAmerica17

    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!
  2. CaptainAmerica17

    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.
  3. CaptainAmerica17

    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.
  4. CaptainAmerica17

    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.
  5. CaptainAmerica17

    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.
  6. CaptainAmerica17

    Need help on a proof from Spivak's Calculus

    Thanks for the hint. It helped a bit.
  7. CaptainAmerica17

    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...
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