Fallacy-explain the point of fallacy

Let a=b so a^2 = ab or a^2-b^2 = ab-b^2 or (a+b)(a-b) = b(a-b) or a+b = b

now, putting the value of a, b+b=b or 2b=b or 2=1 :P But how??

Note by Shubham Sharma
6 years, 5 months ago

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4 votes

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Since a-b=0, in the 4th step you have divided 0 by 0. In mathematics division by zero is meaningless.

Fallacy is an argument built on the base of poor reasoning. Your conclusion might be true or maybe not but it is still fallacious.

Aditya Parson - 6 years, 5 months ago

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yeah, i also got it on wikipedia...

Shubham Sharma - 6 years, 5 months ago

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Instead of a=b, let's let a-b=k

a=b+ka=b+k

a2=ab+aka^2 = ab+ak

a2b2=ab+akb2a^2-b^2 = ab+ak-b^2

(a+b)(ab)=b(ab)+ak(a+b)(a-b) = b(a-b)+ak

a+b=b+akaba+b=b+\frac{ak}{a-b}

You are saying that limx0a×xx=0lim_{x \rightarrow 0} \frac{a \times x}{x} = 0, which causes this fallacy.

Clarence Chew - 6 years, 5 months ago

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dude dats a bit hi-fi!! limit? dats out of range :D

Shubham Sharma - 6 years, 5 months ago

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We are seeing what happens if b is close to a, to determine what went wrong.

Likewise, you cannot evaluate x4x2\frac{x-4}{\sqrt{x}-2} where x=4 directly by substitution, although it is possible to evaluate it. By substitution, we get 00\frac{0}{0} which is kind of meaningless.

Clarence Chew - 6 years, 5 months ago

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@Clarence Chew yup..

Shubham Sharma - 6 years, 5 months ago

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@Clarence Chew That's not meaningless. That is everything. What times 0 equals 0? is what that's asking.

Finn Hulse - 5 years, 7 months ago

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@Finn Hulse I agree that 00\frac{0}{0} can be any number, but the fact that it reduces to 00\frac{0}{0} says nothing more about the value an expression is unless we know that the 00s mean.

Clarence Chew - 5 years ago

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You just can't cut (a-b) as 0/0 is indeterminate.

Vivek Rao - 5 years ago

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a=b means a-b=0, and division by 0 is meaningless.

Kuldeep Guha Mazumder - 4 years, 3 months ago

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