Dec 142011

## Transcendental Numbers

Dec 232010

My mathemagical homie, Noah, once said to me, “If you throw a dartboard at a number line, you’ll hit a transcendental number with probability one.” In laymen’s terms, according to the laws of probability, you will ALWAYS hit a transcendental number. This was surprising to me because at the time I only knew TWO transcendental numbers, e and pi. All the non-transcendentals from the Naturals to the Algebraic Numbers are countable and therefore have measure zero (ie. non-transcendentals are unhittable by the mathemagicians darts). Check out this list of transcendentals on wikipedia. Alot of those guys are just e or pi disguised as sines or logarithms. Yeah, the Gelfond-Schneider theorem gives us infinitely many transcendentals, but only countably infinite. We’ll never hit probability one at that rate. And frankly those other transcendentals, the Champernowne, Chaitin and Prouhet-Thue-Morse constants are demonic, fantastic and insane.

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