- #1
Pacopag
- 197
- 4
Homework Statement
I was just wondering if
[tex]n!=n(n-1)![/tex]
is completely general. Does it hold even for non-integer n?
The factorial function is a mathematical function denoted by the symbol ! and is used to calculate the product of all positive integers from 1 up to a given number n. It is often used in combinatorics and probability to calculate the number of ways to arrange a set of objects or events.
No, the factorial function is only defined for positive integers. It does not hold for non-integer values of n, as there is no concept of taking the product of non-integer numbers.
Yes, there are alternative functions such as the Gamma function and the Pochhammer symbol that can be used to extend the concept of factorial to non-integer values. These functions are commonly used in statistics and mathematical analysis.
No, the factorial function is only defined for positive integers. It cannot be used for negative values of n, as there is no concept of taking the product of negative numbers.
Yes, the factorial function can only be used for relatively small values of n due to the rapid growth of the function. It also cannot be used for non-integer or negative values of n. Additionally, the factorial function can lead to computational errors for large values of n due to overflow of the computer's memory.