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I've been invited to a maths themed Xmas after party. I need to prepare a selection of interesting, and relatively simple fallacious proofs which other guests will try and find the flaw in. I'm trying to avoid very well known ones, of course.

Each proof needs to fit comfortably on a large whiteboard.

Assume undergraduate level of maths knowledge, though the true cause of flaw does not have to be!

A place where i've previously found suitable material is 'Mathematical Fallacies and Flimflam' by Edward J Barbeau. In there is a good example of a simple fallacious proof of 1=2 using telescoping series, which can also be found here (p.2): http://tomlr.free.fr/Math%E9matiques/Fichiers%20Claude/AwebMaths050601/FFF/FFF94_4.pdf

Feel free to share personal favourites, and make it as annoying to spot the flaw as possible!

Y-dog
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1 Answers1

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For $\;n\in\Bbb N\;$ :

$$\begin{align}&n^2=n\cdot n=\overbrace{n+n+\ldots+n}^{n\;\text{times}}\implies\\{}\\ &2n=\left(n^2\right)'=\left(\overbrace{n+n+\ldots+n}^{n\;\text{times}}\right)'=\overbrace{1+1+\ldots+1}^{n\;\text{times}}=n\implies\\{}\\ &2n=n\implies \color{red}{2=1}\end{align}$$

Timbuc
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  • You're supposed differentiate the $n$ in $n$ times to get $$\overbrace{1+1+\ldots +1}^{1\text{ times}} =1$$ so $2n=1$. Duh. – Milo Brandt Dec 18 '14 at 03:48
  • @Meelo I don't get your comment: in the middle of the second line we apply the diffentiation rule of sum, so for each $;n;$ we have $;n'=1;$ and thus we have the sum of $;n;;1$'s – Timbuc Dec 18 '14 at 03:50