Re: Thieves Philosophy 101

[russotto@wanda.pond.com (Matthew Russotto)]

In article <96k5hl$2nrq$1@newssvr05-en0.news.prodigy.com>,
Kelli Halliburton <kelli217@crosswinds.not> wrote:
>
>"olcott" <olcott@qwest.net> wrote in message
>3A89A36D.6EF8FC2@qwest.net">news:3A89A36D.6EF8FC2@qwest.net...
>>
>> So Infinity + 1 < Infinity + 10 ?
>>
>
>I'm sorry; did you really want to start talking about aleph one and
>comparative infinites?

You won't get there with a plus sign.

>Infinites have cardinality among themselves based on the terms skipped.
>Aleph one is the infinite number defined as the number of positive integers.

Aleph-null is the infinite cardinal (there's ordinals as well) defined
as the cardinality of the set of intehers.  Aleph-one is the
first transfinite cardinal.

>There are infinites with cardinalities both greater and smaller than aleph
>one. Example: the set of all even positive integers has a cardinality less
>than aleph one. The set of all even integers, both positive and negative,
>has a cardinality of aleph one + 1 (because zero is introduced).

The set of all even positive integers has a cardinality equal to
aleph-null.  As does the set of all positive integers, as does the set
of all even integers, as does the set of all rationals.


-- 
Matthew T. Russotto                                russotto@pond.com
"Extremism in defense of liberty is no vice, and moderation in pursuit
of justice is no virtue."