In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 6 Dez., 11:07, Virgil <vir...@ligriv.com> wrote: > > > > 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 not enough that all points are present?
It would be, but the critical ones aren't! > > > > 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". > > A unit lenght 1 times aleph_0 is what?
Nonsense! > > > Lengths are distances between two points > > so what two points does WM claim that Aleph_0 is a distance between? > > If aleph_0 is in trichotomy with other quatities, then the length in > question can be smaller or larger than other lenghts.
The issue is whether what WM calls the "sides" of what he calls a "triangle" actually are what he calls them.
And, as so often happens with WM, the answer is "no". A triangle in standard mathematics is required to have three points as its vertices and three finite line segments ending in pairs of those vertices, but the thing WM is talking about has, at best, one thing vaguely resembling a vertex and two things vaguely resembling half-lines but is totally missing anything resembling the other two needed vertices or the needed third line segment.
One wonders what sort of definition of a triangle WM is using when he cannot scare up more than one angle and what sort of a trigon which has no more than two sides..
WM has a casual attitude about meanings that tends to undercut all his arguments, and does so again with this one. > > Regards, WM --