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.
Post by twetch#2936
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.
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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!