Re: found the contradictory flaw in the Euclidean Geometry axioms; #116; 2n

I found the flaw. I am seeking to prove that infinity
does not exist in Geometry nor math as a whole. Since
infinity does not exist in physics, it should be
contradictory in
mathematics. It is best to find the contradiction in
geometry since
human minds are better
equipped to think in terms of shape than in terms of
quantity.

Last night I made a few posts asking Lwalk if there
are
any contradictions in the axioms or whether there are
superfluous axioms.

It struck me today, where the contradiction lies and
is rather subtle,
that noone would have stumbled on it
without having it prefocused in a hunt down of the
contradiction.

And the contradiction is the obverse or reverse of
what
Dedekind defined for infinity as a set. Dedekind
defined
an infinite set as where you can take a proper subset
and place in a
one-to-one correspondence such as all the even
positive integers
matched with all the positive
integers. The flaw of Dedekind was that he did not
have
FrontView of set with BackView, and if he had had
that
concept of Frontview he would have retracted his
definition.

The flaw of Euclidean Geometry is similar to the
Dedekind flaw
definition of infinite set. Only in Geometry we focus
on the Parallel
Postulate that given a line and a point not on the
line there is one
and only one line parallel to the given line. Instead
of proper subset
in Dedekind, for geometry we focus on Line and
Line Ray.

So here is the contradiction of Euclidean Geometry
with its axioms.
Those axioms assume infinity but that
is contradictory, since a line is infinite in both
directions
but a line-ray is infinite in only one direction.

Now taking the Parallel Postulate, and a point not on
the given line,
I can draw from Euclidean Geometry
an infinite number of line-rays emitting from that
point
which are parallel to the given line.

So this sinks the Euclidean Axiomatics as a
contradictory set of
axioms. It sinks it, because it allows infinity but
infinity does not
allow for the Parallel
Postulate.

What can save Euclidean Geometry is overhaul of the
Parallel Postulate that says that lines stop at 266!
the definition of
Finite and where lines are parallel means that a
perpendicular drawn
on one line is a perpendicular on the second line.

The internal contradiction in Euclidean Geometry is
that
it has infinity but that infinity cannot recognize a
line from a line-
ray and that leads to the Parallel Postulate being
self contradictory.

Now there are other axioms in Euclidean Geometry that
also imply
infinity such as the betweenness axiom and they have
to be refurbished
to the 266! Finite definition.


Yes, sir, I found the flaw of Euclidean Geometry. It is subtle and noone
would have known it unless they were specifically hunting down a flaw
using infinity.

The Flaw is this-- Lines versus Line Rays. Euclidean Geometry does not
distinguish between lines that are infinite in two directions and a Line Ray
which is infinite in one direction. However, it should be quite plain to see
that a Line Ray is really a line itself, because all that a line Ray is, is a
FrontView of a infinite Line itself. Or we can take a look at a Line Ray
that goes to negative infinity and thus 0 would be the BackView.

So that the Parallel Postulate of Euclidean Geometry is contradictory for it
would thus say that a bunch of Line Rays emanating from 0 are all parallel to the given L.

So the way to correct this Flaw of Euclidean Geometry is to say that all of
geometry ends at 266! Finite and that Parallelism is defined as perpendicular at a given line when extended is perpendicular to a second line, so that lines and line rays are one and the same.

We have to refurbish the Betweenness Postulate by saying that we connect
anything smaller than 1/(266!).

Thus we rid Geometry of its contradictory nature with its lines, line-rays
and parallel postulate.

Archimedes Plutonium
www.iw.net/~a_plutonium
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies
.

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