# Big O Notation

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Big O Notation by

## 1. A mathematical notation that describes the limiting behavior of a function when the argument tends towards a particular value or infinity.

### 1.1. argument

1.1.1. In mathematics, and argument is a specific input to a function.

1.1.1.1. Functions

1.1.1.1.1. In mathematics, a function is a relation between sets that associates to every element of a first set exactly one element of the second set.

1.1.2. Another name is input or independent variable.

### 1.2. Limiting Behavior of a Function

1.2.1. Asymptotic Analysis

1.2.1.1. In mathematical analysis, asymptotic analysis, also known as asymptotics, is a method describing limiting behaviors

1.2.1.1.1. Limit

## 4. In computer science, big O notation is used to classify algorithms according to how their running time or space requirements grow as the input size grows

### 4.1. Computational Complexity Theory

4.1.1. Computational complexity theory focuses on classifying computational problems according to their inherent difficult, and relating these classes to each other.

4.1.1.1. Computational problems are tasks solved by a computer

4.1.1.1.1. A computation problem is solvable by mechanical application of mathematical steps, such as an algorithm.

4.1.2. One practical role of computational complexity theory is to determine the practical limits of what computers can and cannot do

4.1.2.1. Millennium Prize Problems

4.1.2.1.1. P versus NP