Re: a mathematical question .. unanswered !!!



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


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