In article <c50550cd-6bce-425c-a985-b9e419605161@o5g2000vbp.googlegroups.com>, William Hughes <wpihughes@gmail.com> wrote:
> On Feb 13, 9:03 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > <snip> > > > You cannot discern that two potentially infinity sequences are equal. > > When will you understand that such a result requires completeness? > > Nope > > Two potentially infinite sequences x and y are > equal iff for every natural number n, the > nth FIS of x is equal to the nth FIS of y > No concept of completeness is needed or used. > > E.G, > > we can use induction to show > > x={1,1+2,1+2+3,...,1+2+...+n,...} > > is equal to > > y={(1)(2)/2,(2)(3)/2,(3)(4)/2,...,n(n+1)/2,...} > > > Consider the list of potentially infinite sequence > L1= > 1000... > 11000... > 111000... > ... > > L2= > 111... > 11000... > 111000... > ... > > The diagonals are both > d=111... > > It makes perfect sense to say that there > is no line in L1 that is equal > to d but there is a line in L2 that is equal > to d
And in neither is there a line 000..., the anti-d. --
