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Shapiro inequality: Let $x_1,x_2,\dots, x_n,x_{n+1},x_{n+2}$ be positive real numbers with $x_{n+1}=x_1$ and $x_{n+2}=x_2$. Now the inequality
$\sum_{i=1}^{n} \dfrac{x_i}{x_{i+1}+x_{i+2}} \geq \dfrac{...

Noone beats Mick gets some (the odds are on his side) by V. Chvatal and B. Reed. It is an article about the satisfiability problem, and the title is of course referring to this song. I havn't read the ...

I don't have an answer, but I have spend a couple of hours on it, so here is some of my thoughts on the problem.
In the following I will identify expressions with sets, so $2^n$ corresponds to the ...

Using AC you can construct a (non-continuous) function that intersects any continuous function on any open interval (or even on any set with positive measure).

As already pointed out, the model seems a bit too simple: In reality the students might be able to exclude one or two of the answers, or they might choose Buzz Lightyear, because they think it is a ...

You can even say something much stronger. As Gowers points out, you can reformulate the question as: Does there exist a function that intersect any vertical line, in any open interval? Here you can ...

If you channel is that you can decide if the cion shows head or tail and the pass the coin to your friend with that side up, then the channel has capacity of one bit. This corresponds to your first ...

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