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- Newsgroups: alt.usage.english
- Path: sparky!uunet!zaphod.mps.ohio-state.edu!darwin.sura.net!jvnc.net!princeton!crux!mikulska
- From: mikulska@crux.Princeton.EDU (Margaret Mikulska)
- Subject: Re: quite unique
- Message-ID: <1992Nov19.234008.26718@Princeton.EDU>
- Originator: news@nimaster
- Sender: news@Princeton.EDU (USENET News System)
- Nntp-Posting-Host: crux.princeton.edu
- Reply-To: mikulska@astro.princeton.edu (Margaret Mikulska)
- Organization: Princeton University
- References: <1992Nov18.192304.15503@nas.nasa.gov> <1992Nov18.221451.14168@bcrka451.bnr.ca>
- Date: Thu, 19 Nov 1992 23:40:08 GMT
- Lines: 28
-
- In article <1992Nov18.221451.14168@bcrka451.bnr.ca> nadeau@bcarh1ab.bnr.ca (Rheal Nadeau) writes:
- >In article <1992Nov18.192304.15503@nas.nasa.gov> asimov@wk223.nas.nasa.gov (Daniel A. Asimov) writes:
- >>
- >>Since there are infinitely more real numbers than integers,
- >>perhaps it *does* make sense to say that 1/3 is "more unique"
- >>than the number 2, in the above contexts.
- >
- >Wrong - there are not infinitely more real numbers than integers. If I
- >had my university notes, I could trot out the proof, but in the
- >meantime: there are infinite numbers of integers and of real numbers.
- >"Infinite" being an absolute term, you can't say that one infinite set
- >is larger than the other (and certainly not infinitely larger).
-
- Complete rubbish and utter nonsense, not to mention total ignorance of
- set theory. The cardinality of the set of integers is much smaller than
- the cardinality of the set of real numbers. In set theory there is a
- whole hierarchy of infinities; you very well can say that an infinite set
- is larger than another infinite set, if "large" refers to the cardinality
- of the sets, as it indeed does. If you can show that there are as many
- real numbers as there are integers, we might as well throw out the whole
- mathematics as we know it out of the window. I'm not holding my breath.
-
- I wonder what course your university notes are from ...
-
-
- -Margaret
- mikulska@astro.princeton.edu
-
-