From: Michael Barr <barr@barrs.org>
To: categories@mta.ca
Subject: Re:stupid question?
Date: Wed, 29 Mar 2000 20:32:21 -0500 (EST) [thread overview]
Message-ID: <Pine.LNX.4.10.10003292031390.8039-100000@triples.math.mcgill.ca> (raw)
In-Reply-To: <200003292023.PAA12854@saul.cis.upenn.edu>
It is not even true for additive functions. Take a Hamel base and send
every element of the base to 1.
On Wed, 29 Mar 2000, Peter Freyd wrote:
> M.M. Mawanda asks:
>
> >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.
>
> No it is not true. For example, the function defined by:
>
> f(x) = if x is irrational then 0 else
> if x = p/q where p and q are co-prime then q.
>
next prev parent reply other threads:[~2000-03-30 1:32 UTC|newest]
Thread overview: 3+ messages / expand[flat|nested] mbox.gz Atom feed top
2000-03-29 20:23 stupid question? Peter Freyd
2000-03-30 1:32 ` Michael Barr [this message]
2000-03-29 23:13 Max Kanovitch
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