3 ms·

How is "zero" more of an abstraction than "five" ?

• gizmo686 9y ago
  Zero was invented long after the rest of the natural numbers (to my knowledge this is the case in every culture that independently invented zero). At least in the case of the Greeks, its status was somewhat controversial; I am not sure how other societies viewed it once it was invented.
  • johncolanduoni 9y ago
    If we find out some alien race started using positive numbers and zero at the same time, do they then become the same level of abstraction?
• smhost 9y ago
  It would go something like: > Zero is offensive and ungodly. With "five", at least there's something there to abstract. With zero, there's not even anything! How can nothing be something? Cue angry biting of thumbs
• rafiei 9y ago
  Because typically you'd be building `five` out of `zero`, but that's more of an "implementation detail" rather than a property of `five` or `zero`. Examples are numerous: i. Peano Axioms: (Typically) your initial element is 0 and you'll get 1 by applying the successor function to 0 and 2 by applying that to 1 and so on. ii. Von Neumann's definition of Ordinals: {} is zero and one is {{}} and two is {{}, {{}}} and so on. iii. Conway's definition of Surreal numbers: {|} is zero and { {|} | } is one and so on. iv. Church encoding and many more. P.S. I'm not a logician and don't know whether "more of an abstraction" has any well-defined meaning and not just the meaning that might be inferred by a software developer.