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  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...
  16. K

    Various Proofs Regarding Divisors and Properties of Divisors

    Hello there. I have been reading G.H. Hardy's book "A Course of Pure Mathematics". It is a fantastic introduction to Analysis. I have no problems with the book so far, however, it does assume some knowledge in number theory. I just want to make sure that the following proofs for properties of...
  17. K

    Questions Regarding Nuclear Fusion

    Thank you very much for your response. Honestly, question 2 was the most important for me. I don't care too much for cold fusion as I know about the chemists you speak of. I just don't like it when people place so much certainty on a field we know so little about. We live in a wonderful world...
  18. K

    Questions Regarding Nuclear Fusion

    Say that it becomes possible in the future. What would you say then? I am not suggesting that it is by any means a great area to spend money and resources on, but, suggesting that it is impossible limits the creativity of the mind. I personally hate the word. It clouds the minds of many whom try...
  19. K

    Questions Regarding Nuclear Fusion

    ^^For the above response...I hate the word impossible. I don't see why it can't be done. Maybe not with today's technology but who knows what the future will hold. Also, why is it against PF rules? Are they that high and mighty of themselves that they feel they can simply declare something as...
  20. K

    Questions Regarding Nuclear Fusion

    Sorry about that. I didn't word that correctly. What was meant to be said was "a high energy neutron is released ALONG with an ample amount of energy." In other words, a neutron is released and so is an x amount of energy. Sorry again.
  21. K

    Questions Regarding Nuclear Fusion

    Hello there physicists! I am here to ask a few straightforward questions regarding nuclear fusion accomplished here on Earth. Question 1: How does a magnetic field contain the heat produced by nuclear fusion in the reactor? If we look at the example of Deuterium fusing with Tritium, a high...
  22. K

    Parallelogram Paradox!

    Thank you! I clearly do not think in a direct mannerism...Anyone else left-handed? Thanks again to everyone for your help! I always seem to have problems with the simple math problems, yet I find set theory and linear algebra rather straightforward...
  23. K

    Parallelogram Paradox!

    Sorry. Just realized you said this first! Take the comment I made to "HallsofIvy" and apply it to yourself as well! Thank you!
  24. K

    Parallelogram Paradox!

    HOLY CRAP! Thank you so much. I cannot believe I didn't think of that! It makes so much sense. It doesn't seem like it when you think about it though...You would think that the area remains constant...GEEZ! Math is exciting! Thank you all and especially you! Very simplistic solution! USE LIMITS...
  25. K

    Parallelogram Paradox!

    Yes. But what I am saying is that the angle is less than 90 degrees. All I have done is taken the original rectangle and "Pushed it" so that it went "sideways." I am just wondering why the area would not simply be A*B instead of A*B*sin(theta) because if it were A*B and the angle is less than...
  26. K

    Parallelogram Paradox!

    Hi there! My question involves the area of a parallelogram. Now, I know how to prove the commonly used formula (b*h) very easily, however, there is a formula given on Wikipedia as an alternative that states....Given two sides B and C with angle (theta), B*C*sin(theta)=Area of a parallelogram...
  27. K

    Electromagnetic Radiation and Mediums

    1. Homework Statement Hello there! I have a couple of questions regarding light(EMR) and how it behaves when moving from one medium to another. From what I understand, the frequency of any light wave, when it moves from one medium to another, stays the same. As a consequence of this, the...
  28. K

    Electromagnetic Waves

    Thank you for your help! It is much clearer to me now! I can't wait to learn more advanced physics!!
  29. K

    Electromagnetic Waves

    Thanks for the reply! Unfortunately, I am a bit more confused now. I understand what you mean by charge distribution in a current carrying wire but what is a crystal ion and what if we had a charged particle flowing through space? There would be no charge distribution since an electron with...
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