Quentin Anciaux skrev:
Hi, Le Thursday 15 November 2007 14:45:24 Torgny Tholerus, vous avez écrit :What do you mean by "each" in the sentence "for each natural number"? How do you define ALL natural numbers? What do you mean by "Every" here? Can you give a *non-circular* definition of this word? Such that: "By every natural number I mean {1,2,3}" or "By every naturla number I mean every number between 1 and 1000000". (This last definition is non-circular because here you can replace "every number" by explicit counting.)
I can prove by induction that there exists a biggest number: A) In the set {m} with one element, there exists a biggest number, this is the number m. B) If you have a set M of numbers, and that set have a biggest number m, and you add a number m2 to this set, then this new set M2 will have a biggest number, either m if m is bigger than m2, or m2 if m2 is bigger than m. C) The induction axiom then says that every set of numbers have a biggest number. Q.E.D. -- Torgny Tholerus --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~--- |

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