🚀 go-pugleaf

On 14 Okt., 00:17, Graham Cooper <grahamcoop...@gmail.com> wrote:
> On Oct 14, 7:13 am, William Hughes <wpihug...@gmail.com> wrote:
>
>
>
>
>
> > On Oct 13, 12:39 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> > > On 13 Okt., 15:29, William Hughes <wpihug...@gmail.com> wrote:
>
> > > > So we are agreed that you can have a finished infinity
> > > > of symbols that contains a symbol for every natural number but does
> > > > not contain the symbol oo.  (note that this finished infinity
> > > > does not have a largest element).
>
> > > Of course, if there are no other arguments contradicting it.
>
> > > > The first column contains every natural number
> > > > but does not contain oo, and the diagonal contains every natural
> > > > number but does not contain oo, They are identical.
>
> > > And here is the argument contradicting it:
> > > The third side must also contain every natural number, but does not.
>
> > There is no third side.
>
> > A third side would have to be the last line.
>
> > The fact that a limit, L, of things from the triangle
> > exists does not mean that L is part of the triangle.
>
> >           - William Hughes
>
> This is my spin on the "Infinite Triangle"
>
> using an INFINITE UNION OF SAMPLES
>
> Consider the sequence
>
> +------->... X
> ! <1>
> ! <12>
> ! <123>
> ! <1234>
> v ...
> Y
>
> The length is oo, but the width is finite
>
> So even if you DEFINE A LIMIT FOR Y->oo
> and no limit for X->oo
>
> The fact X=Y still implies (to WM atleast)
> that the FINISHED INFINITY still never exists.

You see it easily by the infinite square. Nobody disputes that it has
infinite lines.
>
> There is one more step required, for X & Y to reach infinity
> the sequences must be formatted as finite samples (prefixes)
> of infinite sequences and you consider the SAMPLES like so...
>
> +------->...
> ! <1...>
> ! <12...>
> ! <123...>
> ! <1234...>
> v ...
>
> Now the UNION of the above INFINITE SET
>
> = N
>
> since each sequence includes the previous sequence an infinite Union
> is possible
>
> and both LIMITS x->oo and y->oo are defined.
>
> Exists(i): i = oo

If completed infinity would exist.
Therefore we can exclude that possibility.

Regards, WM