# Category:Countable Sets

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This category contains results about **Countable Sets**.

Definitions specific to this category can be found in Definitions/Countable Sets.

$S$ is **countable** if and only if there exists an injection:

- $f: S \to \N$

## Subcategories

This category has the following 6 subcategories, out of 6 total.

### C

### I

### R

### S

### U

## Pages in category "Countable Sets"

The following 42 pages are in this category, out of 42 total.

### C

- Cartesian Product of Countable Sets is Countable
- Cartesian Product of Natural Numbers with Itself is Countable
- Countable iff Cardinality not greater than Aleph Zero
- Countable Set equals Range of Sequence
- Countable Set has Choice Function
- Countable Set is Well-Orderable
- Countable Space is Separable
- Countable Union of Countable Sets is Countable
- Countably Infinite Set in Countably Compact Space has Omega-Accumulation Point

### E

### I

### S

- Set is Countable if Cardinality equals Cardinality of Countable Set
- Set is Countable iff Cardinality not greater Aleph Zero
- Set of Even Integers is Countably Infinite
- Set of Finite Strings is Countably Infinite
- Set of Finite Subsets of Countable Set is Countable
- Set of Infinite Sequences is Uncountable
- Set of Local Minimum is Countable
- Set of Odd Integers is Countably Infinite
- Set of Pairwise Disjoint Intervals is Countable
- Set of Subsets of Finite Character of Countable Set is of Type M
- Set which is Equivalent to Countable Set is Countable
- Subset of Countable Set is Countable
- Subset of Countably Infinite Set is Countable
- Surjection from Countably Infinite Set iff Countable
- Surjection from Natural Numbers iff Countable
- Surjection from Natural Numbers iff Countable/Corollary 1
- Surjection from Natural Numbers iff Countable/Corollary 2