Question
The factorial operation, n!, is defined as...
Answers
GPT-4o mini
The factorial operation, denoted as \( n! \), is defined as the product of all positive integers from 1 to \( n \). Mathematically, it is expressed as:
\[
n! = n \times (n-1) \times (n-2) \times \ldots \times 3 \times 2 \times 1
\]
For example:
- \( 5! = 5 \times 4 \times 3 \times 2 \times 1 = 120 \)
By convention, the factorial of 0 is defined as:
\[
0! = 1
\]
This definition helps maintain consistency in various mathematical formulas, including those involving permutations and combinations. Factorials are widely used in areas such as combinatorics, algebra, and calculus.
\[
n! = n \times (n-1) \times (n-2) \times \ldots \times 3 \times 2 \times 1
\]
For example:
- \( 5! = 5 \times 4 \times 3 \times 2 \times 1 = 120 \)
By convention, the factorial of 0 is defined as:
\[
0! = 1
\]
This definition helps maintain consistency in various mathematical formulas, including those involving permutations and combinations. Factorials are widely used in areas such as combinatorics, algebra, and calculus.