Monthly Archives: September 2008

Chomp is a two-player game which is played as follows: The two players, A and B, start with a “board” which is a chocolate bar divided into small squares. With Player A starting, they take turns choosing a square and … Continue reading →

Intuitively, for any property of sets, there should be a set which has as its members all and only those sets such that holds. But this can’t actually work, due to Russell’s Paradox: Let , and then you can derive … Continue reading →

In the book A=B, the authors point out that while the identity is provable (by a very simple proof!), it’s not possible to prove the truth or falsity of all such identities. This is because Daniel Richardson proved the following: … Continue reading →

There are many functions from to that cannot be computed by any algorithm or computer program. For example, a famous one is the halting problem, defined by if the th Turing machine halts and if the th Turing machine does … Continue reading →

Please enjoy the following guest post on differential geometry by Tim Goldberg. A symplectic structure on a manifold is a differential -form satisfying two conditions: is non-degenerate, i.e. for each and tangent vector based at , if for all tangent … Continue reading →