1. Limited time only! Sign up for a free 30min personal 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!

SImple proof question

  1. Dec 15, 2013 #1
    I'm studying Spivak's calculus and I have a really simple question :

    I'm only in the first chapter on "The basic properties of numbers"

    So far, we have the following propostion

    P1 : (a+b)+c=a+(b+c)

    P3 : a+(-a)=(-a)+a=0

    P2 : a+0=0+a=a

    Now, he tries to prove P2 (He doesn't do it for P3, so it's granted) He also says :

    "The proof of this assertion involves nothing more than subtracting a from both sides of the equation, in other word, adding -a to both sides." Now, that I understand

    "as the following detailled proof shows, all three properties P1-P3 must be used to justify this operation." That I don't understand. First, how can you use a proof of something you haven't proven ? Second, when he says all three properties to justify this operation, he means to substract "a" from both sides, right ? If so, I don't understand how they (properties) can be used ...

    He starts with this :

    If a+x=a

    then (-a)+(a+x)=(-a)+a=0

    hence ((-a)+a)+x=0

    hence 0+x=0

    hence x=0

    My comments : For the first line, he starts with the assertion that an equation a+x=a exists. Now, he substract "a" from borth sides and with property 3 the right hand sides equals 0. With property 1 we regroup and cancel with property 3.Now we have 0+x=0 and we subtract zero from both sides to have x=0. Where is property 2 used ? How is subtracting "a" from both sides proven with all three properties ?

    Thank you
     
  2. jcsd
  3. Dec 15, 2013 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    I think you are mistaken when you say this is a proof of P2. He starts with "a+ x= a" and concludes "x= 0". That is NOT "P2". It is a separate theorem completely. His proof uses P1, P2, and P3.
     
  4. Dec 15, 2013 #3
    Yeah, I didn't understand it in the correct way. Thank you !
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: SImple proof question
  1. Simple Proof (Replies: 10)

  2. Simple proof (Replies: 8)

Loading...