* Re: stupid question?
@ 2000-03-29 20:23 Peter Freyd
2000-03-30 1:32 ` question? Michael Barr
0 siblings, 1 reply; 3+ messages in thread
From: Peter Freyd @ 2000-03-29 20:23 UTC (permalink / raw)
To: categories; +Cc: mm.mawanda
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.
^ permalink raw reply [flat|nested] 3+ messages in thread
* Re:stupid question?
2000-03-29 20:23 stupid question? Peter Freyd
@ 2000-03-30 1:32 ` Michael Barr
0 siblings, 0 replies; 3+ messages in thread
From: Michael Barr @ 2000-03-30 1:32 UTC (permalink / raw)
To: categories
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.
>
^ permalink raw reply [flat|nested] 3+ messages in thread
* Re: Re: stupid question?
@ 2000-03-29 23:13 Max Kanovitch
0 siblings, 0 replies; 3+ messages in thread
From: Max Kanovitch @ 2000-03-29 23:13 UTC (permalink / raw)
To: categories
Dear M.M. Mawanda,
> >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]?
The real fun is about a function f such that
f is unbounded in any open interval (c,d), and
in addition to that: f(x+y) = f(x)+f(y).
> Date: Wed, 29 Mar 2000 15:23:16 -0500 (EST)
> From: Peter Freyd <pjf@saul.cis.upenn.edu>
> Subject: categories: Re: stupid question?
>
> 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.
>
^ permalink raw reply [flat|nested] 3+ messages in thread
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