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:(adsbygoogle = window.adsbygoogle || []).push({});

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?

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The fallacy I had read :

[tex]x^2-x^2=x^2-x^2[/atex]which results to 1 = 2

[tex](x-x)(x+x)=x(x-x)[/atex]

[tex]((x-x)(x+x))/(x-x)=x(x-x)/(x-x)[/atex]

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.

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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.

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# Zero divided by zero

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