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.

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TopNewestWell 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.

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