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  1. K

    Equation of an Ellipse.

    Thank you for the quick reply! The equation I was referring to was (x^2/a^2)+(y^2/b^2)=1.
  2. K

    Equation of an Ellipse.

    1. Homework Statement As I was relearning some concepts in calculus, I came across a section on ellipses. What I don't understand is why a and b in the standard equation of an ellipse govern the length of the minor/major axes. Can anyone shed some light? Thank you very much! 2. Homework...
  3. K

    Euclid's Proof for Prime Numbers

    Yes, sorry, I figured this out earlier. Sorry I did not post to say so. I appreciate the time you have taken to explain this to me. Please know that you have helped someone understand even more just how beatiful math can be. Again, I thank you for all your help!
  4. K

    Euclid's Proof for Prime Numbers

    Ok. I understand everything now. Can you just prove to me that if two numbers, say a and b, have the same factor, then their difference is indeed also divisible by that factor. Thank you so much for your help!
  5. K

    Euclid's Proof for Prime Numbers

    I'm sorry but now you've confused me further. What does q/p have anything to do with P=q+P-q?
  6. K

    Euclid's Proof for Prime Numbers

    Thank you very much! All of this makes sense except for one bit. Why MUST p divide the difference of two integers? Also, 1 is divisible by a number but it yields a fraction. Why must the result be an integer? Again, thank you so much for your help. I understand the proof, I just don't...
  7. K

    Euclid's Proof for Prime Numbers

    Oh and why must p divide the difference between P and Q?
  8. K

    Euclid's Proof for Prime Numbers

    So your telling me that the resulting number must be an integer and not a fraction? Also, why can't p divide P and only q?
  9. K

    Euclid's Proof for Prime Numbers

    1. Homework Statement Euclid's proof Euclid offered the following proof published in his work Elements (Book IX, Proposition 20)[1] and paraphrased here. Take any finite list of prime numbers p1, p2, ..., pn. It will be shown that some additional prime numbers not in this list exist. Let P be...
  10. K

    The Range of a Function in Set Y!

    Wow. Thank you for the lightning fast response! Also, I forgot to mention... Merry Christmas to you if you celebrate it and Merry Christmas to everyone else that celebrates it as well! Happy New Year!
  11. K

    The Range of a Function in Set Y!

    1. Homework Statement N/A 2. Homework Equations N/A 3. The Attempt at a Solution I guess I will start here. My question does not necessarily involve equations. In the Calculus book I am currently studying from, I am reviewing some pre-calculus and I came across a section that...
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