Re: Cut a point into two - topological?

Bob wrote:
How do you cut something with zero width? A point is not a set of things
so you can't split the point into two non-empty sets.

A point is not a thing in a physical sense of matter necessarily, it
can be a hole, it can be a center of gravity, and so forth. It is
different from nothing. It has zero width, but a location of zero
width can accomodate lot's of points of zero width, just as zero +
zero = 2 times zero = 3 times zero = zero.
Only when one denies motion at all, one can deny a lot, but then one
cannot do proper math, one cannot even split a set of two elements
into two of one ( one can not even do a proof, as this is a movement
from an assumption to a confirmation).And topolgy is basically about
deformation, about change or movement too.
A geometrical point is denoting a location., as one of its
properties. Here the reference to the other geometrical objects
doesn't change . With movement , given for example with the creation
of solids through rotation by Euclid or with the quadratrix of Hippias
of Elis before Euclid we have moving objects with locations referred
to each other, and a ,,space" where they are moving. A moving point can
leave a ,, trace", which can be regarded with static geometry, if it is
not ,,visiting" the same location twice. A point moving can sweep out a
line, two lines can intersect in one point, the generating points of
the two lines can meet in the intersection at the same time, but they
can also pass through this location-point at the same time.
a =3 * x + 4,
b = 9 * x + 6 ,
when x = - 1/3 then a and b will be equal of value but not the same.
And from this point 3 the points a and b will move on differently,
when x changes value.
With friendly greetings
Hero
PS in our universe, and there is no other, what one considers a point
at rest , as an absolute location, an other one will look at as a
moving point. Archimedes' lever is still unused.

.

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