Does a-a Always Equal a*0 in Any Number System?

[johncena]

Is this True for all no.s??

Is this true for all no.s (a)?
a-a = a*0

 

[Elucidus]

In any number system that has additive and multiplicative identities, additive inverses, and is distributive, yes.

$$a \cdot 0 = a \cdot (0+0) = (a \cdot 0) + (a \cdot 0)$$

This can only be true if $a \cdot 0 = 0$

$$a - a = a + (-a) = 0 \text{ by definition.}$$

--Elucidus