TITLE: What is zero choose one?
QUESTION [6 upvotes]: Algebraically it comes out to be undefined- but if I have zero elements, and I'm asked to pull elements from it, this should just be zero, right?

REPLY [2 votes]: The graphic of the $\Gamma$ or factorial function can be found here : notice how it diverges towards $\pm\infty$ for each negative integer. Indeed, $$n!=\frac{(n+1)!}{n+1}\iff(-1)!=\frac{(-1+1)!}{-1+1}=\frac{0!}{0}=\frac10=\pm\infty$$ $$C_0^1=\frac{0!}{1!(0-1)!}=\frac1{(-1)!}=\frac1{\pm\infty}=0$$