Definitions

from The American Heritage® Dictionary of the English Language, 4th Edition

  • n. The first of the transfinite cardinal numbers. It corresponds to the number of elements in the set of positive integers. Also called aleph-zero.

from Wiktionary, Creative Commons Attribution/Share-Alike License

  • proper n. The first of the transfinite cardinal numbers; corresponds to the number of positive integers, also called natural numbers. Georg Cantor showed that even all the rational numbers could be put in one-to-one correspondence with them, and are therefore countable, enumerable or denumerable.

from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.

  • n. the smallest infinite integer

Etymologies

Sorry, no etymologies found.

Examples

  • Um... without Jesus you only get the aleph-null Eternal Life tm?

    News from the House of Sticks -

  • If aleph-null socks are lost in the laundry, how many pairs of socks does John have?

    The candidate's a dodger, a well-known dodger

  • Martin Gardner, in his review of books by Eli Maor and Rudy Rucker [NYR, December 3, 1987], mistakenly says that "Cantor called the number that counts the real numbers (rational and irrational) aleph-one, or C," and that "Cantor believed that 2 raised to the power of aleph-null is the same as C."

    An Infinity of Points

  • This last designation he applied to whatever cardinal number comes next in order after aleph-null; its identity with C, the number of real numbers or "power of the continuum," is a famous conjecture of Cantor's, his "continuum hypothesis."

    An Infinity of Points

  • Meanwhile, Loki's Tricksters defeated the Anubis Crew "c" to aleph-null to advance to the semifinals of the Demonic Snowball Tournament in Hell.

    Anime Nano!

  • Both sets have a count or cardinality equal to the transfinite number ‎ א ‎ ‪ 0 - aleph-null.

    TierneyLab

  • As for the aleph-null and aleph-one: it was proven that the continuum hypothesis essentially whether the cardinality of real numbers is aleph-one or higher is undecidable in standard set theory, so whether you want to accept it or not, you won’t hit any contradictions.

    Intelligent Design explained: Part 2 random search - The Panda's Thumb

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