Some days ago I read a fallacious algabraic argument which was quite intresting and made me think about such cases, Last night I came up with a technique to make sense out of all those fallacies which include diving by zero... The technique is as follows: lets say: [tex]a/b=A[/atex] [tex]a=bA[/atex] If we take 'b' as zero, "a = 0" as well and 'A' can be anything. As a result: [tex]0/0=A[/atex] where 'A' can be anything. Concludes to two points: 1) Nothing other than zero is divisible by zero, its only zero itself. 2) Zero divided by zero can be anything. Whats the use of these points? ________________________________ The fallacy I had read : [tex]x^2-x^2=x^2-x^2[/atex] [tex](x-x)(x+x)=x(x-x)[/atex] [tex]((x-x)(x+x))/(x-x)=x(x-x)/(x-x)[/atex]which results to 1 = 2 Using the points above and repeating the third step of the falacy we have; [tex](0/0)(2x)=(0/0)(x)[/atex] which means: [tex]v2x=wx[/atex] (where v is A#1 & w is A#2) as we are to keep the equilibrium between the right and left handside of the equation, the relation between v & w is obvious; [tex]w=2v[/atex] by subsituting: [tex]v2x=2vx[/atex] [tex](v2x)/(2v)=(2vx)/(2v)[/atex] which means x = x and no more a fallacy. ____________________________________________ Even if we look from the other point of view; as multiplicaton is the inverse process of division, and that something multiplied by zero is zero so logically zero divided by zero can be anything. I'd be glad for further comments, I know its forbiden to divide something by zero but its fun Why cant we do the process mentioned above? Thanks for giving your time.