As per my understanding positive and negative are just indicative of direction of number axes with zero at the center. If that is the case we should apply same laws to both positive and negative numbers.

But actually we treat negating and positive entirely differently in computation

e.g. negative of negative = positive but positive of positive =positive

Is there anything we are missing ?

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    $\begingroup$ That's like asking "If $\frac12 \cdot 2 =1$, why isn't $1\cdot 1=\frac12$?" $\endgroup$ – MPW Mar 29 '15 at 13:00
  • $\begingroup$ See this explanation with an (appropriate?) interpretation of signs as direction. $\endgroup$ – Pedro Mar 29 '15 at 13:03
  • $\begingroup$ @Pedro: Thanks that was helpful $\endgroup$ – Xinus Mar 29 '15 at 13:07
  • $\begingroup$ If a minus times a minus was a minus, the graph of $y=-x$ would look like a $\Lambda$ instead of a line. If a plus times a plus was a minus, the graph of $y=+x$ would look like a $\rm V$ instead of a line. $\endgroup$ – Akiva Weinberger Mar 29 '15 at 23:07

Why do you think we are treating them differently? We have $$++\to +\\--\to +\\+-\to -\\-+\to-,$$ which has a remarkable symmetry.

And, on top of that, the image: the minus sign is a "make a 180 degree turn" and the plus sign is "don't turn". So, if you have $-(-5)$, you make a turn, then you make a turn, then walk 5 units of length. Two turns of 180 degrees amount to not turning at all.

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Well, I think that the meaning of the algebraic operator is a just a convention based on the meaning applied historically to the minus (-) operator, according to the standard algebra, for that reason a double minus is for instance in terms of money like "a quantity which is not (-) a debt (-)" so by that reason it turns to be a possesion you have (+), but I think that it would be perfectly valid if you define a different meaning for the minus operator, it would be just a different algebra and a different algebraic operation than the standard minus operator of the algebra in use.

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  • $\begingroup$ and same thing for the (+) plus operator, you can redefine it and create your own algebra with your own rules. $\endgroup$ – iadvd Mar 29 '15 at 13:16

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