Yeah, not so sure about that. The factorial is defined on positive integers by induction. What value to assign the base case of 0 is in a sense a free choice, but you know you'll always want 0!=1 for binomial theorem, etc...
Post by twetch#21877
As it turns out, of the countably many continuous extensions of factorial to C, there is a unique meromorphic log convex one called the gamma function, but even she has poles at all negative integers. There really is a problem with thinking -1!=0!/0.
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Thanks for the clarification, I need to read up on my definitions! I'm no mathematician by any means but i do find philosophy of mathematics very interesting.
I would certainly agree. I strongly recommend the book Proofs and Refutations by Imre Lakatos if you haven't read it. It's rather accessible and a gem!