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Incorrect Proof

Take an in-depth look into this proof. Obviously it is wrong. Where is it wrong and why? This is obviously wrong. Where and why? Detailed explanation is needed of where and why it is wrong with all examples. Thanks

Let a = b.

Multiply both sides by a (OK because we don't violate the equal sign). We get a² = ab.

Subtract b² from both sides (again OK because we don't violate the equal sign).

We get a² - b² = ab - b².

Factor the left side. a² - b² = (a + b)(a - b).

Factor the right side. ab - b² = b(a - b).

Set these two factors equal to each other. They started that way, so there's no problem here.

We get (a + b)(a - b) = b(a - b).

Now, divide both sides by (a - b). Again, we're not violating the equal sign.

We're left with a + b = b.

But, we originally set a = b. Therefore, let's replace a with b on the left side of the equation.

We get b + b = b. or 2b = b.

Now, the last step. We divide both sides by b.

The result is 2 = 1!

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Solution Summary

This is an incorrect proof that begins a=b and ends 2=1, then shows where the mistake is.

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