Part 1/5:
Understanding Factorials: A Deep Dive
Factorials are a fundamental concept in mathematics, particularly in fields like combinatorics, probability, and statistics. The notation for factorial is denoted as n!, where n is a positive integer. This article provides a comprehensive overview of factorials, their definitions, recursive properties, and applications.
What is a Factorial?
Factorials can be defined simply: for any positive integer n, the factorial is calculated as the product of all positive integers from 1 to n. For example:
- 5! = 5 × 4 × 3 × 2 × 1 = 120
It is important to note that the factorial function is only defined for non-negative integers. Negative numbers and fractions cannot be utilized in this context.