Recent content by dragonslayer

The fact that 0!=1 is not a convention, it is a mathematical fact (not something we "agreed" on). And his can be proved, as the OP was asking. The Γ function is unique because it shows step by step that 0!=1, without any subjective reasoning. To further my point, we could not have decided...

alright, consider the gamma function: Γ(z)=∫(t^(z-1)e^(-t)dt, 0, infinity) which has the property Γ(z+1)=zΓ(z) (too long to prove, look it up), in turn implying that Γ(z+1)=z! so 0!=Γ(0+1)=Γ(1) Γ(1)=∫(t^(1-1)e^(-t)dt, 0, infinity) =∫(e^(-t)dt, 0, infinity) = -e^(-t), 0, infinity...