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# Begin of lunch box unwrap

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Funny fallacious 'proofs' (ordered by difficulty level);

'Proof' that a dog has nine legs;

A dog has nine legs;

No dog has five legs

A dog had four more legs than no dog

'Proof' that 2 = 1

'Proof' that 1 =  0

$$(n+1)^2 = n^2 + 2n + 1\\ (n+1)^2 -(2n+1) = n^2\\ (n+1)^2 - (2n+1) - n(2n+1) = n^2 - n(2n+1)\\ (n+1)^2 - (n+1)(2n+1) = n^2 - n(2n+1)\\ (n+1)^2 - (n+1)(2n+1)+\frac{(2n+1)^2}{4} = n^2-n(2n+1)++\frac{(2n+1)^2}{4}\\ ((n+1)-\frac{2n+1}{2})^2 = (n-\frac{2n+1}{2})^2\\ (n+1)-\frac{2n+1}{2} = n - \frac{2n+1}{2}\\ n+1 = n\\ 1 = 0\\$$

'Proof' that 1 is the largest number

'Proof' that 1 = -1

$$1 = \sqrt{1} = \sqrt{-1*-1} = \sqrt{-1}*\sqrt{-1} = i*i = i^2 = -1$$

'Proof' that all cars have the same color

Proof by induction

If there is one car, all cars have the same color.

Fix an arbitrary n. Suppose that for any set of n cars they have the same color. Consider any set of n+1 cars. Then car 1 through n have the same color. We also know that cars 2 through n+1 have the same color by the inductive hypothesis. Hence all cars must have the same color.

'Proof' that 0 = 1

Using integration by parts we have

$$\int\frac{1}{x} = x*\frac{1}{x} - \int x d\frac{1}{x}\\ \int\frac{1}{x} = 1 - \int x(-\frac{1}{x^2})dx\\ \int\frac{1}{x} = 1 + \int \frac{1}{x}dx\\ 0 = 1$$

'Proof' that $$e^x = 1 \mbox{ }\forall x$$

$$e^x = exp(i2\pi*\frac{x}{i2\pi}) = exp(i2\pi)^\frac{x}{i2\pi} = 1^{\frac{x}{i2\pi}} = 1$$

Have I just disproven your world?

Jun 18, 2014

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A great post reinout-g.

Jun 18, 2014

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I cant even find a reaction picture for this....

Jun 18, 2014
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A great post reinout-g.

Melody Jun 18, 2014
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looks like the devil is really old !lol!

Jun 18, 2014
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Jun 19, 2014
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Aah, I guess if someone's interested (s)he could try and see where the fault lies in these.

Well thought of Melody

Jun 19, 2014
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Indeed he could!

Jun 19, 2014