clipka <ano### [at] anonymousorg> wrote:
>
> ...As a matter of fact, in its most
> basic form the multiplication operation isn't even /defined/ for
> negative numbers; defining whether the product of two negative values
> should itself be negative or positive is actually a choice -- it doesn't
> follow from first principles (although the choice that such a product
> should be positive turns out to be helpful).
>
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. ;-)

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