```Date: Dec 29, 2012 12:18 AM
Author: Virgil
Subject: Re: CHANGING THE DIAGONAL!

In article <9533c4f1-686c-45be-8ef8-f7f4d3a9eab7@ui9g2000pbc.googlegroups.com>, Graham Cooper <grahamcooper7@gmail.com> wrote:> On Dec 29, 11:37 am, Virgil <vir...@ligriv.com> wrote:> > In article> > <adde38fa-1e63-43a1-94f0-908da37a4...@s6g2000pby.googlegroups.com>,> >  Graham Cooper <grahamcoop...@gmail.com> wrote:> >> >> >> >> >> >> >> >> >> > > +----->> > > | 0. 542..> > > | 0. 983..> > > | 0. 143..> > > | 0. 543..> > > | ...> > > v> > > OK - THINK - don't back explain to me.> > > You run down the Diagonal  5 8 3 ...> > > IN YOUR MIND -> >> > > [1]> > > you change each digit ONE AT A TIME> > > 0.694...> > > but this process NEVER STOPS> >> > > [2]> > > so you NEVER CONSTRUCT A NEW DIGIT SEQUENCE!> >> > That is like saying that the function f+ |N -> |N : x \_--> x^2> > never ends.> > > Right!  but since it has no free variable input to apply it's safe to> extrapolate results toward infinity.> > >> > As soon as one has a completed rule by which values of the function are> > determined from its domain to its codomain, the function is defined.> >> > E.g., f:|N --> |N : 2 |--> 2*x+1> > is  completed function> >> > Thus a rule or function for determining anti-diagonal digits creates the> > entire anti-diagonal list of digits in one step.> >> > dependent on the input.As a function of the input certainly, but one theat function is defined the process is essentially completed.> > In this case, you cannot ANTI-DIAGONALISE an infinite set.> > Every digit you change is substitutable by another digit in another> permutation.I have defined a function which does it automatically for any and every list of endless sequences of decimal digits, giving a resulting sequence not listed in that list.--
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