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- From: jbaez@riesz.mit.edu (John C. Baez)
- Newsgroups: sci.math
- Subject: Re: measures of the `size' of infinite sets
- Message-ID: <1992Sep11.215906.7268@galois.mit.edu>
- Date: 11 Sep 92 21:59:06 GMT
- References: <1992Sep9.042345.7472@galois.mit.edu> <1992Sep9.062701.8487@galois.mit.edu> <1992Sep11.175829.79520@Cookie.secapl.com>
- Sender: news@galois.mit.edu
- Organization: MIT Department of Mathematics, Cambridge, MA
- Lines: 24
- Nntp-Posting-Host: riesz
-
- In article <1992Sep11.175829.79520@Cookie.secapl.com> frank@Cookie.secapl.com (Frank Adams) writes:
- >In article <1992Sep9.062701.8487@galois.mit.edu> jbaez@riesz.mit.edu (John C. Baez) writes:
- >>In article <1992Sep9.042345.7472@galois.mit.edu> jbaez@riesz.mit.edu (John C. Baez) writes:
- >>
- >>> But for your problem the best answer involves not measure
- >>>but "density". Given a set of integers, we calculate its density as
- >>>follows. Figure out how many integers in your set lie between -n and n
- >>>- say that m do. Take the ratio n/2m ... this just tells us what
- >>>fraction of the integers between -n and n lie in your set. Now take the
- >>>limit as n goes to infinity! If the limit exists and equals d (some
- >>>number between 0 and 1), we say your set has density d.
- >>
- >>Okay, I got that one messed up all right. Take the ratio m/(2n+1),
- >>since there are 2n+1 integers between -n and n, counting the endpoints.
- >
- >Since you're taking the limit as n goes to infinity, it doesn't really
- >matter. The limit is always exactly the same either way.
-
- Heh. Take a close look at what I wrote the first time, and you will
- see that even in the limit, it would not give the right answer.
-
- (Someone else, who will remain nameless here, emailed me with the same
- remark. It's a good example of "reading what was meant, not what was
- written.")
-
