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X * 0=0

  1. Jan 28, 2004 #1
    I have to prove that x*0= 0 where x is any integer. I can do this pretty easily using the proposition that m(-1)=-m but I am not allowed to use this. In addition, I am unable to prove m(-1)=-m unless I accept the fact that anything times zero equals zero. Can anyone give me a hint or push on how to show this? I am just going around in circles.
  2. jcsd
  3. Jan 28, 2004 #2

    matt grime

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    0.m=(0+0).m =0.m+0.m

    subtract m.0 from both sides.
  4. Jan 28, 2004 #3
    Thanks, Im an idiot. I kept trying to represent 0 as (m + -m)
  5. Jul 19, 2009 #4
    When x is an integer, multiplication can be defined as:

    [tex]x*a = \sum^x_{n=1} a[/tex]

    When a = 0:

    [tex]x*0 = \sum^x_{n=1} 0 = \underbrace{0 + 0 + ... + 0}_x = 0[/tex]
    Last edited: Jul 19, 2009
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