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Chris Angelico <rosuav at gmail.com>: > On Fri, Jul 7, 2017 at 6:43 PM, Marko Rauhamaa <marko at pacujo.net> wrote: >> Python's integer object 0 might be equated with the (mathematical) >> natural number 18974387634. Python code would have no way of >> introspecting that natural number. >> >> The execution model would determine what properties object 18974387634 >> would have. > > Then what's the point of that number? If you can't see it from Python > code, it's not part of the language semantics. Excellent question!!! In fact, it is a very frustrating question. You can only define the semantics of Python (in this case) by providing an *arbitrary* mapping to an imaginary abstract machine. There's no way to define the objective abstraction. Metamathematicians grappled with the same problem a century ago when they tried to define natural numbers. Their promising start collapsed because of the Russel paradox. To their great disappointment, they had to choose an arbitrary set-theoretical model to be the standard: 0 = {} 1 = {0} 2 = {0, 1} 3 = {0, 1, 2} etc In fact, today's mathematicians couldn't care less what natural numbers are. They have captured all relevant characteristics in a number axioms, and those suffice to generate all interesting mathematics. Marko

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