Sune Jakobsen
  • Member for 12 years, 2 months
  • Last seen more than 5 years ago
Examples of eventual counterexamples
19 votes

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{...

View answer
Most memorable titles
15 votes

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 ...

View answer
Generalizing a problem to make it easier
6 votes

Here is a blog post I wrote about this. I contains three elementary examples of problems from the IMC that you can solve by generalizing.

View answer
Is there a combinatorial interpretation of the identity $\sum_{k=0}^m 2^{-2k} \binom{2k}{k} \binom{2m-k}{m} =4^{-m} \binom{4m+1}{2m}$?
6 votes

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 ...

View answer
Most 'unintuitive' application of the Axiom of Choice?
4 votes

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).

View answer
Estimate rate of real correct/wrong from 4 answers quiz.
2 votes

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 ...

View answer
Function with range equal to whole reals on every open set
1 votes

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 ...

View answer
Channel capacity of a coin flip
Accepted answer
0 votes

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 ...

View answer