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mubashirmansoor
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Some days ago I read a fallacious algabraic argument which was quite interesting 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:
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 :
Using the points above and repeating the third step of the falacy we have;
which means:
as we are to keep the equilibrium between the right and left handside of the equation, the relation between v & w is obvious;
by subsituting:
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 can't we do the process mentioned above?
Thanks for giving your time.
lets say:
[tex]a/b=A[/atex]
[tex]a=bA[/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[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]
[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 can't we do the process mentioned above?
Thanks for giving your time.
Last edited: