(-1)! (Factorial)

Hey Guys, I was just wondering why (-1) factorial is undefined or infinity? Google calculator solves it for (-1), What could be the reason???

Note by Vaibhav Kandwal
3 years, 6 months ago

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Well the factorial is technically defined only for nonnegative integers, just how it works.

A generalization of it into all real numbers is the gamma function. You can look it up, but to give you a small idea, in the gamma function you have the property that \[\Gamma(x)=(x-1)!\] whenever \(x\) takes on a nonnegative integer. If you were interested in computing some sort of \((-1)!\), note that: \[\Gamma(x+1)=x!\] Then a substituion of a \(-1\) on the right would give you \(\Gamma(0)\) on the left, which approaches infinity.

But typically speaking, the factorial, \(x!\) is defined on nonnegative integers only. It's just how it's defined, sort of similar to the concept of even and odd numbers. They're only defined on the integers. The factorial is only define on the nonnegative integers.

Osama Kawish - 3 years, 3 months ago

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