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## #1 2013-08-02 06:44:22

Al-Allo
Member
Registered: 2012-08-23
Posts: 324

### Proof question.

I have a question concerning a proof that two negatives makes a positive :

Here is the outline of this proof: Let us prove first that 3 . (-5)= -15. What is -15? It is a number opposite to 15, that is, a number that produces zero when added to 15. So we must prove that 3 . (-5) + 15=0

Indeed, 3 . (-5) + 15= 3 . (-5) +3 .5 = 3. (-5+5)=3.0=0

(When taking 3 out of the parentheses we use the law ab+ac=a(b+c) for a=3, b=-5, c=5;we assume that it is true for all numbers, including negative ones.) So 3.(-5)=-15

....

One thing which I do not follow is, why the need to prove that -15 is really -15 ? We know that, (-5)+(-5)+(-5)=-15

Logically, I don't see what else it could be But in the above text, are we really trying to show that the number -15 is really -15 by adding it to positive 15 ?So if it really gives 0, we are sure to be in presence of negative fifteen(3.-5=-15) ? Or is there anything that I've missed about it ? ANy help would appreciated ! Thank you.

Last edited by Al-Allo (2013-08-02 06:45:04)

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## #2 2013-11-05 02:06:42

Nehushtan
Member
Registered: 2013-03-09
Posts: 897
Website

### Re: Proof question.

is by definition the additive inverse of
, i.e. the unique integer
such that
.

To prove that an integer is equal to

, add it to 15 and show that it equals zero.

Thus, to prove that

, you need to show that
. That is all the proof is doing. No other properties of
are assumed.

Last edited by Nehushtan (2013-11-05 20:11:25)

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