# Category:Examples of Injections

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This category contains examples of Injection/Definition 1.

A mapping $f$ is **an injection**, or **injective** if and only if:

- $\forall x_1, x_2 \in \Dom f: \map f {x_1} = \map f {x_2} \implies x_1 = x_2$

That is, an **injection** is a mapping such that the output uniquely determines its input.

## Subcategories

This category has only the following subcategory.

### E

## Pages in category "Examples of Injections"

The following 16 pages are in this category, out of 16 total.

### I

- Injection/Examples
- Injection/Examples/2x Function on Integers
- Injection/Examples/2x+1 Function on Integers
- Injection/Examples/Cube Function
- Injection/Examples/Negative Function on Integers
- Injection/Examples/Non-Injection
- Injection/Examples/Non-Injection/Arbitrary Mapping on Sets
- Injection/Examples/Non-Injection/Half Even Zero Odd
- Injection/Examples/Square Function on Natural Numbers
- Integer Square Function is not Injective