Associated Topics || Dr. Math Home || Search Dr. Math

### Aleph Null

```
Date: 01/22/98 at 19:08:14
From: Jonathan
Subject: Aleph null

What does aleph null represent?
```

```
Date: 01/27/98 at 16:19:34
From: Doctor Joe
Subject: Re: Aleph null

Dear Jonathan,

Before I deal with Aleph Null formally, I need to go through some
stuff about sets, first the finite ones, then the infinite ones; and
last of all I shall explain how you measure the size of these sets.

A set is a collection of objects. An object is called an element.

For instance, a class of K students is regarded as a set of students.

Some sets are finite (meaning there is a finite number of elements in
those sets) while some are infinite (for instance the set of all
integers).

If a class of K students has 12 members(or elements), then K has size
12. Technically, we say that the set has order 12 or we say that the
cardinality of the set is 12.

For infinite sets, we are also interested in whether we can somehow
count the objects. Of course, we can never finish listing them. But
what we may do (as best we can) is count the elements by assigning the
natural numbers in a one-to-one way, so as not to skip any members of
the set.

This concept leads us to the formulation of countability.

A set is said to be countable if either it is finite or it can be put
on a one-to-one correspondence with the set of natural numbers
{1,2,3,...}.

For instance, we say that the set of integers is countable since
the following listing demonstrates that there is a one-to-one
correspondence between the set of integers and the set of natural
numbers:

0  1  -1  2  -2  3  -3 ...
|  |   |  |   |  |   |
1  2   3  4   5  6   7 ...

If a set X has a one-to-one correspondence with the set of natural
numbers N, then X is said to have the same cardinality as N.
And the cardinality of N is denoted by the first cardinal number
Aleph Null.

-Doctor Joe,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Sets

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search