aleph-null love

# aleph-null

## 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.

• 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.

• 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

• 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