from The American Heritage® Dictionary of the English Language, 5th Edition.

  • noun The first of the transfinite cardinal numbers. It corresponds to the number of elements in the set of positive integers.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

  • proper noun set theory 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.

  • noun the smallest infinite integer


Sorry, no etymologies found.


  • 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.


  • 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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  • Some notions cause my brain unease;

    The scale of infinity is one of these.

    With weird aleph-null

    It batters my skull.

    Can't we say it's "everything," please?

    December 11, 2014

  • Which leads us to my favorite thing, the continuum hypothesis.

    December 19, 2007

  • A transfinite number, written ℵ0, which denotes the cardinality of the natural numbers.

    In other words, it's a way to express that some infinities are bigger than others.

    December 18, 2007