On 2015-11-29 04:48 AM (-4), Kenneth wrote:
> This particular example-- multiplying two negative numbers and getting a
> positive answer-- has always given me pause, philosophically. That might sound
> strange, coming from someone who considers himself (reasonably) math-literate;
> but I have always had a kind of built-in stumbling-block regarding it's
> 'philosophical basis', and why or how this 'convention' came about, in the
> history of mathematics. ('Convention' may not be the correct way of putting it,
> of course; there have no doubt been many great mathematicians who have struggled
> with this concept in order to put it on a firm logical foundation. I hope!)
>
> Put more simply: It seems perfectly 'obvious' that +3 X +2 = +6 (as any child
> discovers, when making two sets of three toy blocks, for example.) Likewise, -2
> X +3 should 'obviously' produce -6 ... although I can't think of a good
> 'child's' example to illustrate that ;-) But when it comes to -2 X -3, it just
> doesn't seem 'intuitive' that it should produce a positive value. (Although,
> what *else* it should produce is certainly a mystery!) HOWEVER... I'm not about
> to question centuries (millennia??) of mathematical thought-- I'll just accept
> it. ;-)

-2 x  3 = -6
-2 x  2 = -4
-2 x  1 = -2
-2 x  0 =  0
-2 x -1 =  2
-2 x -2 =  4
-2 x -3 =  6

Seems intuitive enough.  I figured this out on my own as a kid, although 
I was suspicious of my own reasoning until it was confirmed in math class.

Post a reply to this message