In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> 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.
Not unless both sides have endpoints other than the one they share. And in WM's whatever-it-is, neither side has one.
> It > is just the (wrong) claim of set theory that aleph_0 is a quantity > that is contradicted here.
WM may be claiming it but set theory does not. Set theory only agrees that the naturally ordered set of naturals (and any set order-isomorphic to it) does not have a "last" member > > We have one side of lenght 1*aleph_0 and the other side of length > sqrt(2)* aleph_0.
Aleph_0 may be either an ordinality or a cardinality, dependent on usage, but is never a "length". Lengths are distances between two points so what two points does WM claim that Aleph_0 is a distance between?
> According to Cantor these are quantities, aleph_0 is > even a "whole number", in English commonly called intteger.
Certainly not by those who use a spell checker.
And also not by those mathematicians (all the the standard ones) who regard each whole number and integer as reachable in a finite number of unit steps from 0. > > > > 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.
In standard geometry, one does not have the complete length of any "side" of any triangle, or any geometric figure, until one has both endpoints.
So WM is doing highly nonstandard geometry, perhaps in his Wolkenmuekenheim in which he commands what the the rules can be, rather than in any place where he has to follow anyone else's rules. > > > > 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.
Not to those who know the difference between geometrical line length and set cardinality. Knowdledge that even freshmen math classes should impose on those who are allowed to pass. > > But matheologians are not that precise.
WM, the prime represetative of that class, certainly isn't.
> In case of matheology they > deny the identity of algebra and geometry.
Actually real mathematics distinguishes between them but WM's WMytheology often is not abel to.
>And in geometry they accept > completed infinity for the height and the diagonal of my triangle.
WM has yet to present sci.math, or anyone else, with any mathematically acceptable triangle having either a geometrically valid vertical side or a geometrically valid diagonal side.
> But > they do not recognize that this would imply completed infinity for the > width of said triangle.
Since the alleged vertical and diagonal "sides" do not exist as sides outside of WMytheology, only those forced to live there, which most of us fotunately are not, need deal with such problems.
> It is only a very minor difference. A > mathematician, however, will also be disturbed by very small errors.
The allegedly small differences are WM's errors. > > Therefore matheology is not a part of mathematics.
And we mathematicians are glad WM's world is no part of it --