Re: a mathematical question .. unanswered !!!


RP wrote:
> Udayan wrote:
>
> > Hi all !
> >
> >
> > We all know very well that..
> > 1) + x + = +
> > 2) + x - = -
> > 3) - x - = +
> > But why ???
> >
> >
> > someone plz tell me the exact logical and mathematical reson for
> > this very basic maths relations..
> >
> >
> > wating 4 ur answers..
>
> Short explanation. Multiplication is just addition/subtraction in
> shorthand.
> 3 * 2 means 0 + 2 + 2 + 2 = 6 or alternately 0 + 3 + 3 = 6
> 3 * (-2) means 0 + (-2) + (-2) + (-2) = -6 or alternately 0 - 3 - 3 = -6
> (-3) * 2 means 0 - 2 - 2 -2 = -6 or alternately 0 + (-3) + (-3) = -6
>
> The set theoretical definition of x is a bit different, but is
> functionally equivalent to the above.
>
> In logical terms, take the sets of elements A and B and form the set of
> all possible ordered pairs. This is called the Cartesian product or
> cross product. The cardinal number of the resultant set ,i.e. n(A x B)
> is the product of the cardinal numbers of the original sets n(A) * n(B).
>
> Example: A = {a,b,c} and B = {1,2}.
> The set of ordered pairs from A x B is
> {(a,1), (a,2), (b,1), (b,2), (c,1), (c,2)}
> which has a cardinality of 6.
>
> Richard Perry

Exact set theory was the resolution also, a cardinal or set of ordered
operands is definable now.

.

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