_Every_ real value? Yes, that's much stronger! And obviously the previous mention of the base-13 function triggered my question, though I thought I hadn't heard of the function before -- the association must have been in my subconscious somewhere. All right, I'm going to have to read up on this miraculous function. (In case anybody was hoping that this topic might lead to interesting visuals -- well, no. I think we can prove that any presentation will just look like a gray blur.) On Tue, Apr 14, 2020 at 12:44 PM Adam P. Goucher <apgoucher@gmx.com> wrote:
Yes, also by the great late J. H. Conway:
https://en.wikipedia.org/wiki/Conway_base_13_function
It's actually stronger than what you've asked for; it takes every real value on every nontrivial interval.
-- APG.
Sent: Tuesday, April 14, 2020 at 5:32 PM From: "Allan Wechsler" <acwacw@gmail.com> To: math-fun <math-fun@mailman.xmission.com> Subject: [math-fun] Extremely discontinuous function
Intuitively, there ought to be a R->R function whose graph is dense in R^2. But I haven't been able to come up with one quickly. Is there a classic example? _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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