Re: Infinity (was Re: Car acceleration)

[Bernard Cleyet <anngeorg@PACBELL.NET>]

I was speaking of the lay use, not the mathematicians'.  Bad usage:  "almost
infinite."

You refer to Aleph null, Aleph one, etc.  Gamow discussed this in "One Two
Three Infinity."

bc

countable means can be put in one to one correspondence with, say, the +
integers (many sets are countable).  More:

http://www.jcu.edu/math/vignettes/infinity.htm


Michael Bowen wrote:

> At 11:15 2002/02/04, Bernard Cleyet wrote:
> > Like unique (and infinite), I thought wrong could not be compared.
>
> I found this comment rather interesting. Are you sure about the
> non-comparability of "infinite"?
>
> I'm no set theorist, but I was under the impression that there were at
> least two flavors (and "sizes") of infinity: the cardinality of the set of
> real numbers ("uncountable") and the cardinality of the set of counting
> numbers ("countable", a peculiar choice of jargon that I have never quite
> understood). The infinities have different "sizes" in the sense that it is
> not possible to set up a one-to-one correspondence between the two number
> sets. I once saw a clever way of setting up a one-to-one correspondence
> between the counting numbers and the rationals (thus showing the set of
> rationals also to be countably infinite), but it was so cute that it has
> since slipped out of my mind.
>
> I'll happily go along with the uniqueness of "unique". :-)
>
> --MB