The inequality states: . This is very easily proved by squaring both sides, and cancelling the common terms. One gets the following on doing this: . For every pair of indices i & j, we can take the two same terms from the RHS and put them onto the...

  If , then for some . Now to evaluate , we know that for some <img src='http://s1.wordpress.com/latex.php?latex=x_2%2C+y_2%2C+kax_2%2Bkay_2+%3D+d%5E%7B%27%7D&bg=ffffff&fg=000000&s=0' alt='x_2, y_2, kax_2+kay_2 = d^{'}' title='x_2, y_2, kax_2+kay_2...

Great to see a site that’s modelled on www.stackoverflow.com. I’ve posted my first question here: http://mathoverflow.net/questions/840/the-core-question-of-topology

Definitions Simplex: Given points in general position, the smallest convex set containing these points is known as the k-Simplex, i.e. points on the simplex are represented as with . i.e. the 0-simplex is a point, the 1-simplex is a line, the...

So for the last few days I’ve been trying to prove the Mobius Inversion formula: If , then . The best way to get an intuitive understanding of this formula is to write out a few equations in long form. For example, I worked out the values of ...