Definitions
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 ofpositive integers , also called natural numbers. Georg Cantor showed that even all therational 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
Etymologies
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Examples
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Um... without Jesus you only get the aleph-null Eternal Life tm?
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If aleph-null socks are lost in the laundry, how many pairs of socks does John have?
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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 Stein, Howard 1988
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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 Stein, Howard 1988
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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! 2010
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Both sets have a count or cardinality equal to the transfinite number א 0 - aleph-null.
TierneyLab 2009
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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 2006
adoarns commented on the word aleph-null
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
seanahan commented on the word aleph-null
Which leads us to my favorite thing, the continuum hypothesis.
December 19, 2007
qms commented on the word aleph-null
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