🚀 go-pugleaf

On Oct 17, 9:01 am, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
> netzweltler <reinhard_fisc...@arcor.de> writes:
> > On 16 Okt., 22:26, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
> >> netzweltler <reinhard_fisc...@arcor.de> writes:
> >> > On 16 Okt., 14:47, William Hughes <wpihug...@gmail.com> wrote:
> >> >> On Oct 16, 5:19 am, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> >> >> > On 16 Okt., 03:51, William Hughes <wpihug...@gmail.com> wrote:
>
> >> >> > > > The  infinite triangle can be constructed in a completely symmetrical
> >> >> > > > way.
>
> >> >> > > Totally irrelevant to the fact that the first column of the
> >> >> > > infinite triangle contains a sequence of
> >> >> > > all natural numbers and no finite triangle contains a sequence of all
> >> >> > > natural numbers.
>
> >> >> > But relevant for the infinite triangle
>
> >> >> Well, until you come up with a relevant  comment to:
>
> >> >>        The first column of the infinite triangle contains a
> >> >> sequence of all natural numbers and no finite triangle contains
> >> >> a sequence of all natural numbers.
>
> >> >> we will take it as read.
>
> >> >> Next, note that the finite triangles
> >> >> 1
>
> >> >> 1
> >> >> 22
>
> >> >> 1
> >> >> 22
> >> >> 333
>
> >> >> all have three sides, while the limit "triangle"
>
> >> >> 1
> >> >> 22
> >> >> 333
> >> >> ...
>
> >> >> has two sides.
>
> >> >>                    - William Hughes
>
> >> > Limit "triangle"??? If at no step of construction (i.e. _never_) there
> >> > are less than three sides, why should there be less than three sides,
> >> > when the triangle is complete?
>
> >> If at no step in the sequence 1/2, 1/4, 1/8, ..., we reach a
> >> non-positive number, why should the limit be non-positive?
>
> >> Limits preserve some features and not others.  In the case discussed
> >> above, we must also be careful to specify what we mean when we say the
> >> limit of the sequence of triangles, mind you.
>
> >> --
> >> "You see, sometimes being delusional is the best way to get that good
> >> idea.  And if you're too afraid to test the limits of sanity, then you
> >> can't be a highly creative person.  That probably explains some of
> >> you."                     -- James S. Harris explains himself, too
>
> > Let's say, I want to construct the list
>
> > 1
> > 11
> > 111
> > ...
>
> > and I am writing this list into the unit square like that:
>
> > t = 0: I am writing 1 to position (0, 1)
> > t = 0.5: I am writing 1 to position (0, 0.5), another 1 to position
> > (0.5, 0.5)
> > t = 0.75: I am writing 1 to position (0, 0.25), 1 to position (0.5,
> > 0.25), 1 to position (0.75, 0.25)
> > ...
>
> > At t = 1 the list is finished. Is this the limit "triangle" we are
> > talking about?
>
> Not really my conversation, but I think this is the limit that they are
> discussing.
>
> Of course, it's still not altogether clear what the limit ought to be
> unless we add some explicit claims:
>
>   A row is in the list at t=1 if and only if it was written at some
>   point prior to t=1.  (No row is written at t=1.)
>
> That should be enough to conclude that, if we number the rows beginning
> with 1, every row will be assigned some natural number.  Moreover, row n
> will consist of n ones.  Hence there is no row with infinitely many
> rows.
>
> Of course, WM is far too stupid to draw this obvious conclusion.  To be
> honest, I'm not sure why William bothers to discuss these things with
> him, but to each his own.
>

I'm sure he follows your proof above that oo-1 = finity!  Clap clap!

Herc