American Heritage® Dictionary of the English Language, Fourth 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.
- n. 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.
- n. the smallest infinite integer
“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.”
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