Table of Contents

## Identity Function

Identity Function – Infinity Learn: Identity function is a mathematical function that returns the same result for any input. It is typically written as ƒ(x) = x, where x is any real number. The identity function graph is a simple line that goes through the origin, with a slope of 1.

## Identity Function Properties

- An identity function is a mathematical function that assigns a unique value to each element in a set. The identity function is usually represented by the symbol “x” and is defined as follows:

x(x) = x

- The identity function is often used in mathematics and computer science to simplify formulas and equations. It is also used in programming to create loops

## Identity Function Examples

### 1. Sorting functions:

The sorting functions are those that take one or more input values and return a sorted output.

Some common sorting functions are:

- Quicksort
- Heapsort
- Merge Sort

### 2. Mathematical functions:

Mathematical functions are those that take one or more input values and return a mathematical result.

Some common mathematical functions are:

- Addition
- Subtraction
- Multiplication
- Division

## Identity Function

- An identity function, or identity map, is a function that assigns each element of a set its own unique identity. The identity function is usually represented by the symbol “Id.” If a function “f” is not an identity function, then it is said to be “not-Id.”
- Identity functions are important in mathematics because they allow us to simplify complex equations. For example, if we want to find the derivative of a function “f” with respect to another function “g,” we can use the identity function “Id” to cancel out the “g” terms. This allows us to more easily find the derivative of “f” with respect to “x.”
- Identity functions can also be used to represent certain concepts in physics and chemistry. In physics, for example, the identity function can be used to represent the concept of a “point particle.” A point particle is a particle that has no size or dimension. In chemistry, the identity function can be used to represent the concept of an “elementary particle.” An elementary particle is a particle that cannot be broken down into smaller particles.