My Math Forum proving -0=0

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 February 19th, 2012, 01:29 PM #1 Member   Joined: Oct 2011 Posts: 31 Thanks: 0 proving -0=0 How do we prove : -0 = 0 ??
 February 19th, 2012, 01:47 PM #2 Member   Joined: Jan 2012 Posts: 47 Thanks: 0 Re: proving -0=0 Hi; as far as I know all equations need to be kept in balance ie what we do on one side must be done on the other. So -0=0 and 0=-0 we add 0 to one side we must subtract it from the other to keep the balance.
 February 19th, 2012, 01:53 PM #3 Member   Joined: Jan 2012 Posts: 47 Thanks: 0 Re: proving -0=0 or if you prefer. -0=0 subtract from both sides gives --0=-0 = +0 =-0 = 0 =-0 Hope this helps.
February 19th, 2012, 02:02 PM   #4
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Re: proving -0=0

Quote:
 Originally Posted by anthonye or if you prefer. -0=0 subtract from both sides gives --0=-0 = +0 =-0 = 0 =-0 Hope this helps.
I cannot follow.

Can you be more clear??

How do you start the proof?

 February 19th, 2012, 02:08 PM #5 Member   Joined: Jan 2012 Posts: 47 Thanks: 0 Re: proving -0=0 Subtracting a negative number is like adding the same corresponding number minus a negative number is the same as adding the same corresponding number --0=-0. does that help.
 February 19th, 2012, 02:59 PM #6 Senior Member   Joined: Jan 2012 Posts: 131 Thanks: 0 Re: proving -0=0 The set of real numbers to the right of 0 is called positive numbers; the set to left of 0 is the set of negative numbers while 0 itself neither positive nor negative
February 19th, 2012, 08:12 PM   #7
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Re: proving -0=0

Quote:
 Originally Posted by azizlwl The set of real numbers to the right of 0 is called positive numbers; the set to left of 0 is the set of negative numbers while 0 itself neither positive nor negative
You mean by definition is : -0 =0 ??

 February 19th, 2012, 08:24 PM #8 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,168 Thanks: 472 Math Focus: Calculus/ODEs Re: proving -0=0 Zero in the only real number without a sign, implied or otherwise. Zero is neither negative nor positive. Positive is defined as greater than zero and negative is defined as less than zero. However, if we try to find a number x whose negative is equal to its positive, we find: $-x=x$  $x=0$ So, we find, among the real numbers at least, that zero is the only number such that -x = x.
February 19th, 2012, 08:36 PM   #9
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Re: proving -0=0

Quote:
 Originally Posted by MarkFL Zero in the only real number without a sign, implied or otherwise. Zero is neither negative nor positive. Positive is defined as greater than zero and negative is defined as less than zero. However, if we try to find a number x whose negative is equal to its positive, we find: $-x=x$  $x=0$ So, we find, among the real numbers at least, that zero is the only number such that -x = x.
I think you have just prove that :

If -x =x then x=0 .

But we want ,-0 =0 ,only

 February 19th, 2012, 08:38 PM #10 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,168 Thanks: 472 Math Focus: Calculus/ODEs Re: proving -0=0 Showing that if -x = x then x = 0, shows that -0 = 0, does it not?

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