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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.

@Finn Hulse
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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.

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This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

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## Comments

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TopNewestSince 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.

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yeah, i also got it on wikipedia...

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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.

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

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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.

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$\frac{0}{0}$ 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.

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

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

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