faktoriáln1

Faktoriáln1, often written as 1!, is the factorial of the number 1. The factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. Therefore, for n=1, the factorial is simply the product of all positive integers less than or equal to 1, which is just 1.

The concept of factorials is fundamental in combinatorics and probability. It is used in formulas for permutations and combinations, which help in counting the number of ways to arrange or select items from a set. While the factorial is defined for non-negative integers, the value of 1! is a direct and simple case.

The definition of the factorial extends to 0! as well, which is conventionally defined as 1. This convention is useful in many mathematical formulas, particularly those involving combinations and power series, where it ensures consistency. For instance, the binomial theorem uses factorials, and the definition of 0! = 1 maintains the validity of the theorem for edge cases.

In summary, faktoriáln1, or 1!, is mathematically equal to 1. It is a straightforward application of the factorial definition and plays a role in various mathematical fields where factorials are employed.