# Category:Sequences

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This category contains results about Sequences.

Definitions specific to this category can be found in Definitions/Sequences.

A **sequence** is a mapping whose domain is a subset of the set of natural numbers $\N$.

## Subcategories

This category has the following 20 subcategories, out of 20 total.

### A

### C

### D

### E

### G

### H

### I

### O

### R

### S

## Pages in category "Sequences"

The following 41 pages are in this category, out of 41 total.

### C

- Cauchy's Convergence Criterion
- Closed Form for Sequence 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, ...
- Closure of Subset of Metric Space by Convergent Sequence
- Compact First-Countable Space is Sequentially Compact
- Composition of Sequence with Mapping
- Constant Sequence Converges to Constant in Normed Division Ring
- Convergence of Sequence in Discrete Space
- Convergence of Sequence in Discrete Space/Corollary
- Convergent Sequence in Normed Division Ring is Bounded
- Convergent Sequence in Set of Integers
- Convergent Sequence in Set of Integers/Corollary
- Convergent Sequence with Finite Number of Terms Deleted is Convergent

### E

### I

- Increasing Sequence in Ordered Set Terminates iff Maximal Element
- Inequality Rule for Real Sequences
- Inertia Principle
- Infinite Sequence in Countably Compact Space has Accumulation Point
- Isometry Preserves Sequence Convergence
- Isometry Preserves Sequence Convergence/Proof 1
- Isometry Preserves Sequence Convergence/Proof 2

### L

### S

- Sequence Converges to Within Half Limit/Normed Division Ring
- Sequence of 7 Consecutive Integers including Multiple of Prime greater than 41
- Sequence on Finite Product Space Converges to Point iff Projections Converge to Projections of Point
- Strictly Increasing Sequence induces Partition
- Strictly Increasing Sequence of Natural Numbers
- Strictly Increasing Sequence on Ordered Set