```Date: Feb 7, 2013 2:54 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Matheology § 222

On 7 Feb., 08:15, fom <fomJ...@nyms.net> wrote:> On 2/7/2013 12:45 AM, WM wrote:> > For every n: (a_n1, a_n2, ..., a_nn) =/= (d_1, d_2, ..., d_n).> > For every n: (a_n1, a_n2, ..., a_nn) is terminating.> > For every n: (d_1, d_2, ..., d_n) is terminating.>> > For all n: (a_n1, a_n2, ..., a_nn) =/= (d_1, d_2, ..., d_n).> > For all n: (a_n1, a_n2, ..., a_nn) is terminating.> > For all n: (d_1, d_2, ..., d_n) is *not* terminating.> that the irrational number, in virtue of> the property given to it by the definitions> has just as definite a reality in our minds> as the rational numbers or even the integers,> and that one does not even need to gain it> through a limiting process, but by possession> of it one becomes convinced of the practicability> and evidence of limiting processes in> general.">> Notice the word DEFINITION in Cantor's> statement.Definition or not - all cases have to be treated similarly: "for all"either expresses a limit or not. There is not a bit of logic inarbitrary choice.Cantor said: Die transfiniten Zahlen stehen oder fallen mit denendlichen Irrationalzahlen. (The transfinite numbers stand or fallwith the finite irrational numbers.) He should have said they stand orfall with the *complete decimal representations* of irrationalnumbers.> That is how LOGIC is applied> in the FOUNDATIONAL STUDY of DEMONSTRATIVE> SCIENCES.-In the logic applied in mathemaics "for every" is tantamount to "forall". Instead of blatheríng in capitals you should apply logicalthinking. Sorry if I demand an impossibility.Regards, WM
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