Re: Is one-to-one mapping valid for comparing infinite-sized sets?

On Sep 18, 9:26 pm, MoeBlee <jazzm...@xxxxxxxxxxx> wrote:
On Sep 18, 6:45 am, venkat.6...@xxxxxxxxx wrote:



Ofcourse, it is like trying to find a bijection between a school of
fish and the water in which they swim. R is a medium in which the
numbers (or points) float. I think we have a poor understanding of R
and think it is a set of discrete entities. There is no such set,
because points won't make up an extent (see below). Also when we move
a point P from zero to one, nothing special happens as it goes through
the intervening points. it goes through rationals, irrationals,
transcendentals etc with same ease. Human perception of these points,
seen through the rationals, attaches all strange characteristics to
these innocent points. All points are same in every geometrical sense.
Any peculiarities have to be blamed to our yardstick.

Points wont make up an extent because extent and points are mutually
invertible objects. One defines the other. Actually one can only be
defined through the other, and one exists because of the other. If
points make up extent, then extent is lost but points remain. This
can't happen since you can't define points without extent.

Those are ramblings of someone ignorant of the basics of the subject.
Why don't you read how mathematicians have actually dealt with this
subject?

No wonder it sounds like a rambling to you, because may be you can
process only the usual math discussion. I would like to think outside
the established math framework in this case. Do you want to refute my
thoughts on point and extent? To start with, since there is no
adjacency between the points in R, the extent around a point is always
unfilled. Also, if the extent vanishes around a point, the point
itself vanishes because it can no longer cut the extent into two, and
it coincides with its adjacent one. This alone shows that extent is
not made up of points. In other words, the continuum is NOT a set of
points. Now, what is R? Is it the continuum or a set of points? It
can't be both. However, when you attempt the bijection of R with Q,
you start with notion that R is a set of points, but while trying to
find the bijection, you assume it is continuum by filling the extents
with new points unendingly and unsuccessfully. This is the problem, I
think.



MoeBlee

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