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Topic: Provenance of a function
Replies: 5   Last Post: Nov 5, 1995 9:03 PM

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John Conway

Posts: 2,238
Registered: 12/3/04
Re: Provenance of a function
Posted: Nov 5, 1995 9:03 PM
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On Mon, 30 Oct 1995 wrote:

> Does anyone know the provenance of the following function which is
> discontinuous on the rationals in [1,2] but continuous on the
> irrationals? Does it have a name? Who is credited with defining
> it?
> Define the function h: [1,2]-->R as follows:
> h(x) = 0 if x is irrational
> h(x) = 1/n if x is rational and x = m/n, where m and n are positive
> integers with no common factors.
> I came across the function in an exercise set in the book
> _Real Analysis_ by Patrick Fitzpatrick, with no reference to other
> source.
> Joel Lehmann
> Dept. Math & CS
> Valparaiso University

I don't know the provenance of this function, which has been
a staple of real analysis courses for many years. However, I DO
have a name for it, that I've been using for the last 30 years,
and that some (who must have got it from me) put into a book,
namely "Stars over Babylon". To see why the name is appropriate,
draw a fairly accurate picture!

John Conway

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