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Topic: Matheology § 244
Replies: 3   Last Post: Apr 10, 2013 7:11 PM

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 mueckenh@rz.fh-augsburg.de Posts: 18,076 Registered: 1/29/05
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

Date Subject Author
4/10/13 mueckenh@rz.fh-augsburg.de
4/10/13 me 154934
4/10/13 fom
4/10/13 Virgil