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

In article
<5d8d2df2-3da5-4ea4-8ee2-c1513ccca6cf@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
venkat.6123@xxxxxxxxx wrote:

On Sep 19, 11:12 am, David Bernier <david...@xxxxxxxxxxxx> wrote:
venkat wrote:
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

[...]

"Since there is no adjacency between the points in R,
 the extent around a point is always unfilled."

So:

"There is no adjacency between the points in R.
 Therefore, the extent around a point is always unfilled."

So:

"If the extent around points were ever filled,
 then some points in R would be adjacent."

Is that true according to you?

Yes, if "filled" means "filled by points".

Do you mean that the midpoint between two points need not always be a
point?


Since the extent around a point is always
unfilled, then ... what could come next?

Its the extent !!! right next to every point.

What comes next AFTER that extent? The same extent again, repeating
itself endlessly? That is what you seem to be saying.


David Bernier
.

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