Re: Extrapolating linear ratios

On Dec 18, 1:51 pm, WM <mueck...@xxxxxxxxxxxxxxxxx> wrote:
Every finite subset of even numbers has density 1/2 or less. Simply
divide the required interval by the number of even integers.

THERE IS NO required interval.
Good grief. If you mean the difference between the biggest element
and the smallest one THEN SAY that.
The point being that IF you ever got around to defining anything
accurately, IT WOULD JUST BE IMMEDIATELY CLEAR why everything
you are saying about infinity is bull***.

What is the density of the even numbers IN THE WHOLE INFINITE set of
naturals?
Last we heard, the fact that YOU CAN'T DEFINE this was provoking you
to allege
that this infinite set DID NOT EXIST. But that IS NOT a proof.

You seem to think that the fact that the WHOLE set has the SAME number
of even
numbers AS IT HAS PRIME numbers and AS IT HAS SQUARE numbers and
AS IT HAS POWERS OF 2 proves that there is some sort of contradiction
going on.
THERE JUST ISN'T. You are perfectly free to define some OTHER measure
of the size of infinite subsets of infinite sets IF you mistake
yourself for
competent to do that. But even if you could do that consistently
(which of course
you can't), that STILL wouldn't change the fact that since YOU AGREE
WITH US
that the bijection-equivalence criterion works FOR SIZES OF ALL FINITE
sets,
it THEREFORE-ACCORDING*TO*YOU* ought TO ALSO work for infinite ones.

.

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