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??

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Comments

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 - 8 years, 1 month ago

yeah, i also got it on wikipedia...

Shubham Sharma - 8 years, 1 month ago

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

$a=b+k$

$a^2 = ab+ak$

$a^2-b^2 = ab+ak-b^2$

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

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

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

Clarence Chew - 8 years, 1 month ago

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

Shubham Sharma - 8 years, 1 month ago

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

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

Clarence Chew - 8 years, 1 month ago

@Clarence Chew – yup..

Shubham Sharma - 8 years ago

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

Finn Hulse - 7 years, 3 months ago

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

Clarence Chew - 6 years, 8 months ago

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

Vivek Rao - 6 years, 8 months ago

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

Kuldeep Guha Mazumder - 5 years, 11 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$