Re: Infinity can not exist

From: Tracy Yucikas (tyucikas_at_nethere.com)
Date: 07/12/04 

Date: Sun, 11 Jul 2004 23:29:21 -0700

"Robert J. Kolker" <robert_kolker@hotmail.com> wrote in message
news:8ESHc.45385$JR4.25009@attbi_s54...
>
>
>
> Inifinite cardinality of sets is very well defined. A set has infinite
> cardinality if it can be mapped 1-1 onto a proper subset of it self.

Robert,

if (0,3) is the continuous interval (real numbers) between 0 and 3 without
the endpoints included and
[0,3] is the interval between 0 and 3 WITH the endpoints included

is (1,2) a "proper" subset of [0,3] ?

I ask because I don't think a 1-1 mapping exists between
open interval and closed intervals, tho both seem to possess infiinite
cardinality

a simple 1-1 mapping existts between (1,2) and (1.1, 1.9) so it has infinite
cardinality
likewise between [0,3] and [1,2] so it also has infinite cardinality

I realize that your definition didn't say "any" proper subset, but maybe
this is a side issue. Are there differences between the cardinality
of an open interval and a closed interval?

And if you know of a straightforward 1-1 mapping between open and closed
intervals I'd be very grateful to see it.

thank you,
tracy
(been a long time since thinking about this sort of thing\)

> Consider, for example, the set of non-negative integers Z. n <-> 2*n
> is a 1-1 map of the non-negative integers onto to the even integers
> which is a proper subset of the non-negative integers. Hence Z (by
> definition) is infinite. A set has finite cardinality if it does not
> have infinite cardinality which defines finite and finiteness for
> counting the number of elements in a set.
>
> Infinity is alive and well in the realm of transfinite numbers and set
> theory.
>
> Bob Kolker
>

Relevant Pages

  • Re: Epistemology 201: The Science of Science
    ... >>for counting and determining Cantorian cardinality, ... It shows that two sets can have the same cardinality, ... including all members of the proper subset, ... Why should it not be true of infinite sets? ...
    (sci.math)
  • Re: Epistemology 201: The Science of Science
    ... >>for counting and determining Cantorian cardinality, ... It shows that two sets can have the same cardinality, ... including all members of the proper subset, ... Why should it not be true of infinite sets? ...
    (sci.cognitive)
  • Re: Epistemology 201: The Science of Science
    ... >>for counting and determining Cantorian cardinality, ... It shows that two sets can have the same cardinality, ... including all members of the proper subset, ... Why should it not be true of infinite sets? ...
    (sci.physics)
  • Re: Distinct linear orderings on Z
    ... >>And then at some point this led us to deciding that cardinality and ... >>meant for an infinite set to have a certain number of elements. ... always goes hand in hand with subtraction. ... Does the interval on the reals have to include 1? ...
    (sci.math)
  • Re: Epistemology 201: The Science of Science
    ... Allan C Cybulskie said: ... > is to insist that they both have an infinite set of elements ... ... >> sets have the same cardinality. ... The suggestion that a proper subset by definition has fewer elements was ...
    (sci.math)