1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Spivak Calc: Is my proof correct?

  1. Sep 24, 2011 #1
    1. The problem statement, all variables and given/known data
    Prologue Chapter 1. Problem 8.

    3OEq7.png

    (P10) Trichotomy law: For every number a, one and only one of the following holds:
    (i) a = 0
    (ii) a is in the collection P
    (iii) -a is in the collection P
    (P11) If a and b are in P, then a + b are in P
    (P12) If a and b are in P, then a x b is in P.

    3. The attempt at a solution

    P10: Let (b-a) be any number d. Then P'10 reduces to
    i) d = 0
    ii) 0 <d
    iii) 0 >d
    This is in essence what P10 is, except with the variable being different

    P11: Let there be numbers a, b, c, d.
    If a<b and c<d, then by P'12 the following are true:
    1) a+c < b+c
    2) b+c < b+d
    By P'11, a + c < b + d
    Looking at the case where 0 < b and 0 < d, b + d > 0 which is P11.

    P12: If 0 < a and 0 < c, by P'13, 0 < ac, which is P12
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?