In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 6 Dez., 18:56, mstem...@walkabout.empros.com (Michael Stemper) > wrote: > > In article > > <8fdbfffe-9ad4-4409-a70a-f26497c59...@o6g2000yql.googlegroups.com>, WM > > <mueck...@rz.fh-augsburg.de> writes: > > > > >On 5 Dez., 19:54, mstem...@walkabout.empros.com (Michael Stemper) wrote: > > >> In article > > >> <0e301358-0106-4609-b628-14da5781d...@4g2000yql.googlegroups.com>, WM > > >> <mueck...@rz.fh-augsburg.de> 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?
The lie is in calling things without two endpoint "sides". And even WM SHOULD have learned better in elementary school, but clearly did not. > > > > From Wikipedia: > > > > "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.
I note that WM acknowledges that those sides are required to be COMPLETE, But in his example they are not, since they both lack endpoints at their other (not in common) ends. > > > > 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.
But it does seem to imply that those two sides determine the three points, since a tri-angle requires three vertices, one for each of three angles, and three sides (line segments with two endpoints each)) but WM's whatever it is has only one vertex and what he calls sides do not have two endpoints.
> Never learned logic?
ASk yourself that question rather than asking those whose posts are more logical than your own. > > > 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.
But not necessarily longer than a line of 2*aleph_0 units.
> Or understand that this all is > Cantor-humbug in arithmetic too.
For every non-negative real, x, it is true that x < 2^x, so why be so surprised about it when x is NOT a non-negative real number? > > > 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?
A more proper question is "What third side?"
WM has yet to show that his vaguely angular but non-triangular "thing" HAS a third side. --