In mathematical logic, Gödel's β function is a function used to permit quantification over finite sequences of natural numbers in formal theories of arithmetic. The β function is used, in particular, in showing that the class of arithmetically definable functions is closed under primitive recursion, and therefore includes all primitive recursive functions. == Definition == The β function takes three natural numbers as arguments. It is defined as β(x1, x2, x3) = rem(x1, 1 + (x3 + 1) · x2) = rem(x1, (x3 · x2 + x2 + 1) ) where rem(x, y) denotes the remainder after integer division of x by y (Mendelson...

Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an American mathematician, electrical engineer, and cryptographer known as "the father of information theory". Shannon is noted for having founded information theory with a landmark paper, A Mathematical Theory of Communication, that he published in 1948. He is, perhaps, equally well known for founding digital circuit design theory in 1937, when—as a 21-year-old master's degree student at the Massachusetts Institute of Technology (MIT)—he wrote his thesis demonstrating that electrical applications of Boolean algebra could construct...

The Hardest Logic Puzzle Ever is a logic puzzle so called by American philosopher and logician George Boolos and published in The Harvard Review of Philosophy in 1996. Boolos' article includes multiple ways of solving the problem. A translation in Italian was published earlier in the newspaper La Repubblica, under the title L'indovinello più difficile del mondo. It is stated as follows: Three gods A, B, and C are called, in no particular order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter...