Results 1 to 2 of 2

Math Help - Need help

  1. #1
    Jun 2013

    Question Need help

    Hi everyone, I am studying calculus right now from a book called ''The Principles of Mathematical Analysis'' by Walter Rudin

    The subject is Real and Complex number systems. And I didn't understand some paragraphs.I attached a picture, you can see there the paragraph.I understood the first 3 paragraphs where he proves that p2=2 there is no rational p that satisfies because if p=m/n=2 , a rational number m can be divided by 4 and n can be divided 2 therefore it's not a rational number according to the definition of rational number.

    Now the part that I didn't really understand is after that , the paragraph that starts ''We examine the situation closely..'' and the rest of the text. I didn't understand how he came to those 2 equations that defined p and q. And how he proved that there is a q>p in group A and in group B there is q<p.

    I would appreciate if someone can help me understand this part.Thanks.
    Attached Thumbnails Attached Thumbnails Need help-math-question.png  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Sep 2012

    Re: Need help

    Hey davidciprut.

    They are just using the constraints listed (i.e. p^2 < 2). Note that (p^2 - 2)/(p+2) = (p-2). It is just a clever way of picking a q such that you can pick a p that satisfies the properties for q (making q < p or p > q).

    They picked a q in terms of a p where by they can apply the constraints and prove the result. The particular decomposition they used was picked solely to prove what they were intending to prove.
    Follow Math Help Forum on Facebook and Google+

Search Tags

/mathhelpforum @mathhelpforum