Wednesday, August 25, 2010

Futurama's Math Jokes

Those that love math will probably get a kick out of Futurama and their blink and you miss it math jokes.

Aleph-Null Plex as a theater name instead of a "multiplex." Now that's good. For those that don't know, Aleph-Null is a part of Set Theory, a mathematical concept described in the 1870s by Georg Cantor, a concept that is taught even at simple levels by the use of Venn diagrams (remember those?). According to him there are various types of infinities, and because Cantor was Jewish, he described by the Hebrew letter Aleph.

Aleph-Null (or Aleph-Zero) is used to describe the set with the smallest cardinality (or size of the elements in a set). It measures an infinity according to natural, ordinary counting numbers (excluding zero, negative numbers, and irrational numbers). Cantor made a distinction between transfinite and absolute infinity, in the sense that transfinite numbers are sets bigger than any finite set, yet they fall far short of absolute infinity. In fact, it's been demonstrated at least in classical cardinal mathematics that the sum of all ordinal numbers can't possibly exist, something called the Burali-Forti Paradox.

Think of the Burali-Forti Paradox like this. Take something that is meant to represent the sum of all ordinal numbers. Cantor was partial to the Omega symbol for religious reasons. Now, the concept you just created has all the properties of a number that can be listed in a set! There are some interesting ways to resolve this paradox, notably through use of different principles of set theory.

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