### Is any mathematical term for integer number for which factorial is evaluated?i

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It is interesting is any mathematical term for the integer number for which factorial is evaluated?
That is n! is called factorial and is written as factorial( n ). And what is the name of n? Is any common acceptable term for n?
The questian arised when I wanted to name a function that returns n for a given value of factorial( n ).
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I think you can call n a variable, or a argument.
Thanks, Peter87

But in my opinion a variable or an argument are too general notions. I thought that there is a more specific term for argument of factorial.

Could it be for example a degree or is it a wrong term?
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I guess you could call it a permutation - I just Googled "wiki factorial" & found this page

 http://en.wikipedia.org/wiki/Factorial

Hope this helps
I think a permutation would generally apply to a set of numbers.

Could it not just be operand?
@iHutch105

 I think a permutation would generally apply to a set of numbers.

I agree with you.

As for operand it is not a very expressive term for the name of such a function that returns n.
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¿You mean the inverse function?
This is from the above web page:

 Its most basic occurrence is the fact that there are n! ways to arrange n distinct objects into a sequence (i.e., permutations of the set of objects).

I guess this is combination of what iHutch105 and I are saying.

You could have a set of permutations from a set of objects.

This all talks about factorial n, as for n itself, it would just be number of objects in the set.

The other thing is what application is the factorial for? Eg Terms in a series, but the factorial function is a general one (independent of the application), so I guess you could call it whatever you want.

Perhaps another way of looking at it, is that n is one of the set of positive whole numbers.

A final thought: what about - base ?

@ne555

Is gamma a common acceptable term for integer number for which a factorial is evaluated?
Then how to name the maximum integer number for a given C/C++ integer type for which a factorial can be evaluated?
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I think you may be looking for the term operand.
@TheIdeasMan

 A final thought: what about - base ?

I also thought about base. But is there the term base factorial numbers in mathematics? Will it confuse a user?
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factoriand

 But is there the term base factorial numbers in mathematics?

Well the wiki page didn't have anything at all about what n was referred to as. Does that mean there isn't a term for n?

 Will it confuse a user?

Could you come up with a sentence to describe it like : "Calculate the factorial for this number" You could put that on your form if it is a GUI app, and put it in a tooltip, or say whatever you want if it is a console app.

I guess you have to be careful with the psychology of users, but I wonder if there is some point where you have to assume some reasonable inteligence.
 factoriand

Did you just invent a new word? I like new inventions.
-- is any mathematical term for the integer number for which factorial is evaluated?
-- Don't know specific for the factorial. Generalizing, it's a function so its argument might be called argument.

-- I wanted to name a function that returns n for a given value of factorial( n ).
-- So you created the inverse function of the factorial. You may call it inverse_factorial

wikipedia wrote:
In mathematics, the gamma function (represented by the capital Greek letter Γ) is an extension of the factorial function,
Well, I have called them as argn() and max_argn().
At first I marked the question as resolved but now I have decided to remove the mark because I have some doubts due to an alternative variant.

So there are two proposals. As I showed in the previous post it could be

argn(); // returns a current value of factorial( n )
max_argn(); // returns the maximum acceptable value for a given factorial

and

base(); max_base();

which have the same meaning as the functions above them.

So what is the better?

I am interested espesially the opinion of English spoken programmers.
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Honestly, they're all bad. If you're not going to use ne555's suggestion of 'inverse_factorial', 'factoriand' seems like the most descriptive choice.
I do not know such a word as "factoriand".
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