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!

Prove that

  1. Nov 15, 2004 #1
    x=--x

    wtf =/

    (this isn't a homework problem but it was brought up today and I'm curious) :confused:
     
  2. jcsd
  3. Nov 15, 2004 #2

    NateTG

    User Avatar
    Science Advisor
    Homework Helper

    Well, what do you start with?
    If you start with
    [tex]-1 \times -1 = 1 [/tex]
    then
    [tex]--x = -1(-1(x))=(-1 \times -1) x= 1 x =x[/tex]
    The first equality is by definition, the second because multiplication is associative, the third because you know [itex]-1 \times -1 =1 [/tex] and the last because 1 is the multiplicative identity.

    To see that [tex]-1 \times -1 =1[/tex]:
    [tex]\frac{-1}{-1}=1=\frac{1}{1}[/tex]
    so
    [tex]\frac{-1}{1}=\frac{1}{-1}[/tex]
    but
    [tex]1=\frac{-1}{-1}=-1 \times \frac{1}{-1}=-1 \times -1[/tex]
     
  4. Nov 16, 2004 #3

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    It's a bit easier than that.
    By definition of zero, x+0=x
    By definition of the additive inverse,
    x+(-x)=0

    --x, that is, (-(-x))
    fulfills therefore:
    (-x)+(-(-x)=0
    Add x on both sides:
    x+(-x)+(-(-x))=x, or, since x+(-x)=0, we get:
    (-(-x))=x

    That is the additive inverse to the additive inverse of x is x itself.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Prove that
  1. Prove This! (Replies: 26)

  2. Prove this (Replies: 1)

  3. Proving an equation (Replies: 1)

  4. Proving an Inequality (Replies: 3)

Loading...