What is the process of finding an answer to this; 1.5!=? (or 3/2!) calc ans.=1.32934038817913702047362561250586... (eg 6!=6x5x4x3x2x1=720) (Do you have to make a graph using whole number factorials and use that to fill in the values for decimals? Is it even valid to calculate the factorial of any decimal like[2.53!] ?) Why is it that zero divided by zero is undefined and not just zero or infinity?
The generalization of the factorial to non-integer arguments is called the Gamma function. In general you have n! = Γ(n+1) for n integer. When you ask your calculator to find (3/2)! it is calculating Γ(5/2). Check wiki for more details http://en.wikipedia.org/wiki/Gamma_function
Physics Monkey is correct about the factorial of non-integer numbers. Another good reference is http://mathworld.wolfram.com/Factorial.html Regarding your other question, 0/0 is always officially undefined. However, you can take the limit of a function as it approaches 0/0. For instance consider the function f(x) = sin(x)/x. At x = 0, this is 0/0, but consider values near 0, e.g. f(.1) = .998, as you get arbitrarily close to x = 0 f(x) gets arbitrarily close to 1. So does that mean that 0/0 = 1? If you follow a similar line of reasoning for f(x) = x^2/x you find that as x gets arbitrarily close to 0 then f(x) gets arbitrarily close to 0. So does that mean that 0/0 = 0? With f(x) = x/(x^2) instead you get f(x) getting infinitely large as x gets close to 0. Does that mean that 0/0 = infinity? So basically, 0/0 is undefined because, depending on the exact details of how you get 0/0, you could reasonably call it 0, infinity, or any number in between. There is no one answer that makes sense for all cases. -Hope that helps Dale
