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Matheology § 244
Posted:
Apr 10, 2013 4:23 PM


Consider the diagonal d = d_1, d_2, d_3 ... of a Cantor list, constructed by some appropriate substitution of digits d_n =/= a_nn. For instance, if a_nn > 5 let d_n = 2, and if a_nn < 6 let d_n = 8.
If we have: For all n: d_n is an even digit. Can it be then, that d contains any odd digit?
If we have: For all n: d_1, d_2, ..., d_n all digits are even. Can it be then, that d contains any odd digit?
If we can prove: For all n: d_n has property P. Can it be then that there is a digit with the property ~P?
If we can prove: For all n: d_1, d_2, ..., d_n have the property P. Can it be then that there is a digit with the property ~P?
Cantor speaks of the Inbegriff (set) of all positive numbers n, which should be denoted by the symbol (n). Does that differ from what we denote by N or "all n in N"?
Zermelo requires a set that with a also contains {a}. What is the difference to an inductive set that can be put in bijection with N?
Zermelo defines identity: If M c N and N c M, then M = N.
Is the diagonal d an ordered set of all digits d_n such that the inbegriff (d_n) differs from the set {d_n  n in N}?
Regards, WM



