"Kenneth" <kdw### [at] gmailcom> wrote:
>
> This particular example-- multiplying two negative numbers and getting a
> positive answer-- has always given me pause, philosophically....
> ...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!)

Hey, I've come up with my own 'comfortably' intuitive way of understanding this
concept!

Take a negative number,  say -2

Now I want to negate that negative number:  -(-2)

There are two ways of 'seeing' or understanding -(-2)  The first is simple
'cancellation' of the signs (!). Because, since the leading negative sign is
just a symbol with no numerical quantity attached, the RESULT has to be *a*
value of 2, with some kind of unknown-for-now sign. But the result can't be the
original -2... if it was, then the leading minus-sign would have no purpose at
all(!) Not logical! So, therefore, the result needs to be positive... since it
can't be anything else, dammit! (well, it could *possibly* be zero, by a
quasi-physical rule...i.e., 'forcing' the -2 to go back toward zero on a number
line.... but I'll ignore *that* result...)

The other way of looking at it is as simple multiplication: the 'naked' negative
symbol  '-'  times -2. Even though this operation *in itself* is the
'non-intuitive' crux of the matter, the RESULT needs to be the same as with the
'cancellation' example above...  +2 ...  with no need to do any further
conceptualizing!

SO... Following from this 'equality of operations', it now seems obvious that
multiplying a negative with a negative equals a positive! Voila!

My little April Fool's joke, in December  :-P  Who says amateur philosophers
can't be brilliant?!

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