[lit-ideas] R is not N
- From: Adriano Palma <Palma@xxxxxxxxxx>
- To: "lit-ideas@xxxxxxxxxxxxx" <lit-ideas@xxxxxxxxxxxxx>
- Date: Mon, 10 Jun 2013 07:47:34 +0000
dear Speranza, it is most unfortunate that you keep spreading nonsense -aleph0
is a "proper name" (namely the name of such cardinality)
what you call infinity is, to use the vernacular, many things. One of the major
contributions of the 19th century (with Zermelo, Cantor, and others) was
precisely to show that "infinity" is not a number, viz. the diagonal arguments
that show there is no mapping (or if you want to be picky, oneone
correspondence, which is bijc, etc.) between the infinity of N (the naturals,
1,2,3 ...) and the infinity of R (the reals, there you find a sequence that can
be represented by all rationals plus our friends like "pi" (read in Greek if
you wish)
Best regards
-----Original Message-----
From: lit-ideas-bounce@xxxxxxxxxxxxx [mailto:lit-ideas-bounce@xxxxxxxxxxxxx] On
Behalf Of Robert Paul
Sent: 10 June 2013 07:00 AM
To: lit-ideas@xxxxxxxxxxxxx
Subject: [lit-ideas] Re: Grice's Realm
JL writes
> Cfr. "Infinity", or as mathematicians prefer,
> "∞"
> and "א" (aleph).
These symbols are _not_ equivalent. And you've left out 'Aleph null,' or 'Aleph
sub-naught,' as my grade school English teacher used to say.
This is א with zero as a subscript, an image I can't produce with the current
technology. It denotes the smallest infinite cardinal number.
There's a useful image of it (which could be blown up to poster size) at
<http://en.wikipedia.org/wiki/Aleph_null#Aleph-naught>
Perhaps there's a use for א alone (other than its use as a representation of
the first letter of the Hebrew alphabet), but I can't do the math to determine
if there is.
This is a quote from the Wiki article.
'The aleph numbers differ from the infinity (∞) commonly found in algebra and
calculus. Alephs measure the sizes of sets; infinity, on the other hand, is
commonly defined as an extreme limit of the real number line (applied to a
function or sequence that "diverges to infinity" or "increases without bound"),
or an extreme point of the extended real number line.'
Robert Paul,
The Cantor Institute
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