Is p + pz = p? (1) p = 0 (2) z = 0

Hi Harikrushna Kotadiya!

p+pz = p is true if, and only if, p(1+z)=p is true

This is perfect (and marvellous, see my post above)!

But the following stage: p(1+z) = p implies 1+z=p/p is wrong, because p IS zero, and you cannot divide both sides of the equation in bold by p because of that!

In fact, to divide an equation by ANY unknown value (a "letter", a "variable"), you must be sure it cannot assume the zero value... got it?

Example:

\(abc = {b^2} + \frac{{4bc}}{d}\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,ac = b + \frac{{4c}}{d}\,\,\,\) only if b is different from zero!

(Important: we IMPLICITLY assume d is not zero, otherwise one of the parcels on the left equation - therefore the whole equation - would not have meaning...)

Regards,
Fabio.