On Thursday, December 5, 2013 12:25:24 AM UTC-7, WM wrote: > Am Donnerstag, 5. Dezember 2013 08:18:02 UTC+1 schrieb Virgil: > > > > You used an existential statement, namely: > > > > There exists a certain property of d that cannot be derived from any d_n. > > Whether or not something like d is in the rationals-complete list can only be judged by means of the d_n - at least in mathematics. >
How can we judged the properties of a given object based the properties of a set of others object which the given object is not a member of?
Its like saying are cats are feline, hence my dog is a feline.
> > > What is the reason for this strange behaviour? > > > Because d is not one of the d_n, it can have properties that none of > > them can have, like not being one of them. > > The property of differing or not depedns on the d_n only. Note that Cantor's diagonal argument only uses the d_n. >
The property of differing depends on All place values of the decimal representation of d.