From: "Wendt, Michael - SSMD/DMES" <michael.wendt@statcan.ca>
To: categories@mta.ca
Subject: RE: stupid question?
Date: Wed, 29 Mar 2000 16:48:16 -0500 [thread overview]
Message-ID: <2C04611DA826D311A66D00902715763B0760C2@msxa4.itsd.statcan.ca> (raw)
How about the following?
f(x) = 0 if x is irrational and
f(a/b) = a, where a/b is a fraction in lowest terms
Certainly within any open interval, there are rationals of arbitrarily large
numerator.
For a function that is not bounded above or below, how about:
f(x) = 0 if x is irrational
f(a/b) = a if b is even
f(a/b) = -a if b is odd
-----Original Message-----
From: M.M. Mawanda [mailto:mm.mawanda@nul.ls]
Sent: March 29,2000 4:08 PM
To: cat-dist@mta.ca
Subject: categories: stupid question?
I have been asked the following question: Is it true that any function
defined in a real number closed interval [a,b] (there is not a hypothesis
of continuity) is bounded in an open subinterval (c,d) of [a,b]? My
spontaneous was NO. Unfortunately I cannot find a counter-example to
disapproved my answer. Can someone help.
next reply other threads:[~2000-03-29 21:48 UTC|newest]
Thread overview: 4+ messages / expand[flat|nested] mbox.gz Atom feed top
2000-03-29 21:48 Wendt, Michael - SSMD/DMES [this message]
-- strict thread matches above, loose matches on Subject: below --
2000-03-29 23:13 Max Kanovitch
2000-03-30 3:00 ` Todd Wilson
2000-03-29 20:23 Peter Freyd
2000-03-29 17:36 M.M. Mawanda
Reply instructions:
You may reply publicly to this message via plain-text email
using any one of the following methods:
* Save the following mbox file, import it into your mail client,
and reply-to-all from there: mbox
Avoid top-posting and favor interleaved quoting:
https://en.wikipedia.org/wiki/Posting_style#Interleaved_style
* Reply using the --to, --cc, and --in-reply-to
switches of git-send-email(1):
git send-email \
--in-reply-to=2C04611DA826D311A66D00902715763B0760C2@msxa4.itsd.statcan.ca \
--to=michael.wendt@statcan.ca \
--cc=categories@mta.ca \
/path/to/YOUR_REPLY
https://kernel.org/pub/software/scm/git/docs/git-send-email.html
* If your mail client supports setting the In-Reply-To header
via mailto: links, try the mailto: link
Be sure your reply has a Subject: header at the top and a blank line
before the message body.
This is a public inbox, see mirroring instructions
for how to clone and mirror all data and code used for this inbox;
as well as URLs for NNTP newsgroup(s).