Date: Feb 26, 2013 11:52 AM
Author: David DeLaney
Subject: Re: Problems with Infinity?

Frederick Williams <> wrote:
>Don Kuenz wrote:
>> beginner's language, Cantor uses two sets to define two levels of
>> infinity. One set, Aleph-0, holds countable infinity. The other set,
>> Aleph-1, holds continuum infinity,

>That the cardinality of the continuum (c = 2^{aleph_0}) is equal to
>aleph_1 is Cantor's continuum hypothesis which modern set theory settles
>neither one way nor the other.

Stronger than that - it's provable that it CAN'T settle it one way or another,
unless you extend the theory one way or another (Axiom of Choice, etc., as
Brian already noted).

>> which includes Aleph-0, along with
>> every possible arrangement of Aleph-0. The infinities of complex
>> variables belong to both sets, as does every other common infinity
>> found in mathematical literature.

>Surely not.

Right - "large cardinals" are extremely bigger than either one, and set
theory these days contains a good bit of work on them.

\/David DeLaney posting from "It's not the pot that grows the flower
It's not the clock that slows the hour The definition's plain for anyone to see
Love is all it takes to make a family" - R&P. VISUALIZE HAPPYNET VRbeable<BLINK> - net.legends FAQ & Magic / I WUV you in all CAPS! --K.