For integer x only, is x! considered a polynomial?

  • Thread starter tgt
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  • #1
tgt
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For integer x only, is x! considered a polynomial?
 

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  • #3
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well,
x! = x * (x - 1) * (x - 2) * ... * 2 * 1

And for any integer x! = n where n is some integer.

So, is an integer a polynomial?
 
  • #4
HallsofIvy
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well,
x! = x * (x - 1) * (x - 2) * ... * 2 * 1

And for any integer x! = n where n is some integer.

So, is an integer a polynomial?
That's a strange response! For any integer, x, x2= n where n is some integer.
Is an integer a polynomial? No, of course not. But that has nothing at all to do with whether or not x2 is a polynomial, which it is.

x!, for x a positive integer is not a polynomial but for a very different reason: because it does not satisfy the definition of "polynomial".
 
  • #5
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From Wikipedia:
A function ƒ of one argument is called a polynomial function if it satisfies

for all arguments x, where n is a nonnegative integer and a0, a1,a2, ..., an are constant coefficients.

I think integer fits this definition since n is allowed to be 0, no?
 
  • #6
HallsofIvy
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Yes, you can think of the constant function, whether or not it is an integer, as a polynomial. But that still has nothing to do with the question. Surely you are not confusing a function with a value of the function?
 
  • #7
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I would think that is exactly what I am doing. I apologize tgt if I mislead you.
 

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