>>13962473>Otherwise there would be an annoying inconsistency.Now you're doing math like a physicist! As was demonstrated here
>>13962439there are problems with extending the domain to 0, and is why the gamma function doesn't have 0 in its domain. The point of my comments was to highlight to you that you are (unduly) assuming certain things when you argue that 0! = 1. It's not a definition out of convenience, it's a misunderstanding of the function itself.
And as I argued from the beginning, there is not a single mathematical function for the factorial for which 0 is in its domain. Feel free to search the literature. If you think you have one, feel free to publish it. Because mathematicians would love a rigorous argument for defining 0!.
