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. It is just the (wrong) claim of set theory that aleph_0 is a quantity that is contradicted here.
We have one side of lenght 1*aleph_0 and the other side of length sqrt(2)* aleph_0. According to Cantor these are quantities, aleph_0 is even a "whole number", in English commonly called intteger. > > 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.
That is not of interest here. If you have one angle and the complete lengths of its sides, then you have constructed a perfect triangle - in geometry. > > If you can't specify real coordinates for the vertices, they don't exist, > and you do not have a triangle.
What you say sounds, if translated from geometry into algebra (and you certainly know that both are only different languages for the same contents): If you can't specify a last number in N, then N has no cardinality.
But matheologians are not that precise. In case of matheology they deny the identity of algebra and geometry. And in geometry they accept completed infinity for the height and the diagonal of my triangle. But they do not recognize that this would imply completed infinity for the width of said triangle. It is only a very minor difference. A mathematician, however, will also be disturbed by very small errors.
Therefore matheology is not a part of mathematics.