Re: Cantor Confusion

On Thu, 7 Dec 2006 03:00:21 -0500, David Marcus
<DavidMarcus@xxxxxxxxxxxxxx> wrote:

Bob Kolker wrote:
MoeBlee wrote:
In the sense you're trying to get across to the other poster, I
understand your point. But, just for the record, in a technical sense
in set theory, as integers, rational numbers, and real numbers are
themselves sets, it does make sense to say whether one of them is
countable or not. For example, where integers are defined as
equivalence classes of natural numbers, each integer is itself a
denumerable set. I am not necessarily endorsing anything the other
poster has said; I'm just adding the technical note that in a strict
set theoretic sense, even numbers are sets and thus it is meaningful to
talk about the cardinality of a number.

an element of a ring or a semi-group is a set?

If you use ZFC (or something similar) as your foundation for
mathematics, then everything is a set. Of course, while solid
foundations are good to have, if you are living on an upper floor, you
may prefer to ignore what is going on in the basement.

So you're saying that set "theory" is all of mathematics? Of course
since what you say isn't necessarily true that's not exactly a ringing
endorsement of set "theory".

~v~~
.

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