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 numberscould 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?
If aleph-null socks are lost in the laundry, how many pairs of socks does John have?
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."
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."
Meanwhile, Loki's Tricksters defeated the Anubis Crew "c" to aleph-null to advance to the semifinals of the Demonic Snowball Tournament in Hell.
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.