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

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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.