Date: Dec 7, 2012 12:47 PM
Subject: Re: Matheology § 170

On 6 Dez., 18:56, (Michael Stemper)
> In article <>, WM <> writes:

> >On 5 Dez., 19:54, (Michael Stemper) wrote:
> >> In article <>, WM <> writes:
> >1
> >11
> >111

> >> >In mathematics a triangle is defined by one angle and its two sides.
> >> No, in mathematics a triangle is defined by either its three vertices or
> >> its three sides. Two rays with a common endpoint define an angle, but not
> >> a triangle.

> >Two *sides* with an angle defined by these sides define a triangle.
> Repeating a lie doesn't make it true.

Have you never learned geometry in elementary school?
> From Wikipedia[1]:
>   "A triangle is one of the basic shapes of geometry: a polygon with
>   three corners or vertices and three sides or edges which are line
>   segments."

Just that can be constructed by one angle and two complete sides.
> and:
>   "In Euclidean geometry any three points, when non-collinear, determine
>   a unique triangle [...]"

That does not deny that an angle and two sides determine a triangle.
Never learned logic?

> Both of these refer to the need for three vertices; neither of them says
> that one is enough.

First try to understand that a line of length aleph_0 units is shorter
than a line of lengths 2^aleph_0 units. Or understand that this all is
Cantor-humbug in arithmetic too.

> Something with rays, as WM proposes, would not be a "closed plane figure",
> which all of these competing definitions require.

You have to distinguish between potential and completed infinity. Of
course the sensible definition of potential infinity does not allow to
construct that triangle. But it also gives no quantity for the height.
Complete infinity gives a quantity for the height, which can be
surpassed. Therefore the question is: What about the third side? Has
it a width of aleph_0 units too?

Regards, WM