# Incorrect Proof

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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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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 = ...

###### Education

- BSc , Wuhan Univ. China
- MA, Shandong Univ.

###### Recent Feedback

- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"

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