Date: Dec 5, 2012 1:54 PM
Author: Michael Stemper
Subject: Re: Re: Matheology § 170

In article <>, WM <> writes:
>On 5 Dez., 08:05, Virgil <> wrote:

>> > This set has, like many mathematical entities, a geometrical and an
>> > alytical property:

>> > 0.1
>> > 0.11
>> > 0.111
>> > =A0...
>> > It is a triangle and it is a sequence too.

>> While parts of it can be triangular by reason of having 3 finite sides,
>> the whole of it does not have a third finite side so is not a triangle.
>> NOte that to be a triangle, it would also have to have three vertices,
>> which is not the case.

>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.

If you have two triangles, you can use the lengths of two sides and the
angle between them to see if they are congruent. But, that only works
if you start with two triangles.

If you can't specify real coordinates for the vertices, they don't exist,
and you do not have a triangle.

Michael F. Stemper
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