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  1. CaptainAmerica17

    I Help Finding the Correct Approach to this Proof (Intro Real Analysis)

    Ok, so here is what I have so far: Suppose ##T_1## is infinite and ##\varphi : T_1 \rightarrow T_2## is a bijection. Reasoning: I'm thinking I would then show that there is a bijection, which would be a contradiction since an infinite set couldn't possibly have a one-to-one correspondence...
  2. CaptainAmerica17

    I Proof about injectivity

    I typed this up in Overleaf using MathJax. I'm self-studying so I just want to make sure I'm understanding each concept. For clarification, the notation f^{-1}(x) is referring to the inverse image of the function. I think everything else is pretty straight-forward from how I've written it. Thank...
  3. 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!
  4. 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...
  5. CaptainAmerica17

    Programs Don't like my calculus class, but want to be a math major...

    I am currently a junior in high school and recently, my guidance counselor has been asking me a lot of questions about what I want to major in. Within the last 6-8 months, I have been leaning heavily towards a math major. That was until I started my calc class this year... I'm in AP Calc BC...
  6. CaptainAmerica17

    B Spivak's Calculus as a Prerequisite for General Topology

    High school student here... Recently, I've found an interest in topology and am trying to figure out the correct path for self-studying. I am familiar with set theory and some concepts of abstract algebra but have not really studied any form of analysis, which from what I've read is a...
  7. CaptainAmerica17

    Schools Getting a mathematics mentor in high school?

    High school student here... Over the past year or so, I've developed an intense interest in mathematics. I work problems every day and I am constantly working to grow my knowledge. As a junior, I am currently in AP calculus and will most likely be eligible for Calc 3 my senior year. I'm...
  8. CaptainAmerica17

    Electronics Best way to scavenge parts for a robotic arm?

    I'm a bit new to DIY robotics and for one of my first projects, I want to build a robotic arm. I'm still thinking out the plan for it, but I'm going to need to start gathering parts. Does anyone know of the best way to get parts if you don't have immediate access to a 3D printer? Does anyone go...
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