The Hahn-Banach theorem, Menger’s theorem, and Helly’s theorem « What’s new […] Helly’s theorem, linear programming, Menger’s theorem, minimax theorem, separation theorem In the previous post, I discussed how an induction on dimension approach could establish Hilbert’s […] Reply ...
By applying this structure theorem, we can show that all measurable tilings of the one-dimensional torus are rational, in the sense that lies in a coset of the rationals . This answers a recent conjecture of Conley, Grebik, and Pikhurko; we also give an alternate proof of this conjecture...
It was a known fact that Fermat's little theorem can be used as a primality test. If for a given number b, b Á mod b then b is with high probability a prime number. Unfortunately, an infinite set of exceptions to this primality test exists. A table of exponents then can...
Only by miraculous accident would pulling one lever (for instance, abolishing private property) accomplish all three optimally (you see the mathematical character of Tinbergen's Theorem). Each lever can have a calculable effect of this or that size on all three of the goals, but there must be...
The former happens for instance when lies on the north pole , are points on the equator with longitudes differing by 90 degrees, and is also equal to the north pole; the latter occurs when is instead placed on the south pole. The Cayley-Menger and spherical Cayley-Menger determinants look...