Recent content by kripkrip420

  1. K

    How Should I Proceed?

    Thank you very much for your response Micromass. I actually started doing a lot of work in Spivak's book and the exercises are fun, there is no question. However, as soon as I opened Hardy's or Rudin's books, I just find the building of the Real numbers and the introductions to Set Theory so...
  2. K

    How Should I Proceed?

    Hello there! I will be studying Mathematics and Physics in University in approximately 2 months. I really enjoy Mathematics and have done some introductory Calculus. I have looked into Spivak's book "Calculus" and, although written very well, I just tent to find Calculus boring. However, when...
  3. K

    Verification of Simple Proof

    I understand what you mean. But I notice that it also does not change the outcome if I change the assumption from false to true. I must have made an error somewhere else because I made a similar proof a while back and had it verified by another forum. I will post another proof once I get back...
  4. K

    Verification of Simple Proof

    Hello micromass. I did the proof through contradiction. If we begin with the assumption that the equation is false and manipulate the equation so that everything we do is justifiable, we should end up with a result that varifies the assumption. However, what I got (after showing after steps of...
  5. K

    Verification of Simple Proof

    Okay. I will redo it here and explain myself better. In Spivak's book, he lists 12 properties of the real numbers. I will use those properties to prove that for any real a (a*0)=0. Begin with the assumption that the above statement is false. Since (a*0) is in R, then by the closure...
  6. K

    Verification of Simple Proof

    Please reread the edited proof. I made an error when I first posted.
  7. K

    Verification of Simple Proof

    1. Homework Statement I am using Spivak's Calculus and just finished the third exercise in part 1. It was a very easy exercise but it seems that Spivak makes some assumptions. The problem is as stated: If x^{2}=y^{2}, then either x=y or x=-y. Prove it. The proof was relatively simple (by...
  8. K

    Various Proofs Regarding Divisors and Properties of Divisors

    How can one have Physics without Mathematics? Love them both. Thank you again for your help and (perhaps more importantly) your time. As I read through Spivak's book, I will likely find myself on this wonderful site once again. I hope we bump into each other (in whatever ways one could "bump"...
  9. K

    Various Proofs Regarding Divisors and Properties of Divisors

    Okay. Sounds good. Thank you very much and thanks for the wonderful recommendations for books. By the way, I like your remake of Oppenheimer's quote (or rather, the Bhagavad Gita). Is it safe to assume that you are either a physicist, a physicist in progress, or a polymath?
  10. K

    Various Proofs Regarding Divisors and Properties of Divisors

    Well, what I have applied to is a double major in Mathematics and Physics. I want to become a theoretical physicist as I have a great passion for the study of nature. However, that said, I also very much enjoy pure mathematics. My knowledge in the area of mathematics extends through elementary...
  11. K

    Various Proofs Regarding Divisors and Properties of Divisors

    Thank you again. Now, I have a few final questions. Forgive me for bothering you but I have no guidance. I notice that in a lot of these books, a lot of knowledge in other fields of mathematics is assumed. I am not yet in university and I have no structure in the subject or an order in which to...
  12. K

    Various Proofs Regarding Divisors and Properties of Divisors

    Okay. Thank you very much! I realize that saying it is not enough. I was just wondering why the site did not move forward in showing that the converse was in fact true. Is it considered acceptable to not state such a thing in a proof that relies on such an argument?
  13. K

    Various Proofs Regarding Divisors and Properties of Divisors

    Hello, I found the following proof on a website for proposition 3. http://www.cut-the-knot.org/Generalization/RationalRootTheorem.shtml When the proof is completed it states "so a and bc are coprime". Now I noticed that what was done was a factorization of the expression in the form...
  14. K

    Various Proofs Regarding Divisors and Properties of Divisors

    I apologize. I did not look at the definition of contrapositive. Again, I found the "proof" online and wanted to move quickly in proving proposition 3. I assumed converse and contrapositive were equal. My mistake. I will post a proof of proposition 3 in a moment obviously without the use of...
  15. K

    Various Proofs Regarding Divisors and Properties of Divisors

    Why do you first say "I'm sure it was extremely simple" and then go on to state "only sad that the proposition isn't true"? That makes no sense. The contrapositive I talk of was found online. Assuming that proposition 1 is true, proposition 2 can be "proven" as follows. Assume α does not...
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