Math Is Fun Forum

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Factorial of Decimal Number

I know that, for example, 3! = 3 x 2 x 1 or 6.
What happens when we take the factorial of a decimal number?

Show how to compute the value of (2.5)!

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: Factorial of Decimal Number

Factorial is only defined for whole numbers.  There is a thing called the gamma function.  See what wolfram says.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Factorial of Decimal Number

Factorial is only defined for whole numbers.  There is a thing called the gamma function.  See what wolfram says.

Bob

Ok. Thanks.

Here is what the AI app tells me:

Unfortunately, you can't calculate the factorial of a decimal number like 2.5. Here's why:

* **What's a factorial?**  The factorial (represented by the symbol "!") means multiplying a whole number by all the whole numbers less than it down to 1. For example: 5! = 5 * 4 * 3 * 2 * 1 = 120

* **Why not decimals?** Factorials are defined based on the concept of counting and arranging whole objects. You can't have 2.5 objects to arrange, which is why the factorial of a decimal number isn't defined.

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: Factorial of Decimal Number

I don't really recommend taking information from AI agents seriously. Wikipedia, books, blogs and static websites are a much better source.

Yes, the concept of Factorial is related to counting. But for certain purposes, it makes sense to extend it to real numbers (decimal numbers, as you call them). The Gamma Function is one such function.

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'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.