Talk:Thomae's function

message: I don't have enough analysis books to do a comprehensive count, but in every book I have, this is called Thomae's Function. I know it isn't that big a deal, but "popcorn function" is so terribly informal, whereas "Thomae's function" falls in line with so many other functions whose names are called "[name]'s function" or "[name] function" or similar. Look at List of mathematical functions and tell me how many are named after people vs how many are named after food that they (apparently) resemble. Even the closest relative to this function is named properly, as the Dirichlet function (although it is in nowhere continuous function due to a merge of some sort). That section in the list includes several functions of this exact type (canonical examples/counterexamples in elementary analysis), all of which are named after people. So anyway, sorry about rambling a bit, I propose that we move it to Thomae's function, and redirect this page there. I just feel like maybe next we'll move Error function to ski-slope function (yes, I know, I'm being sarcastic). Any opinions? --Cheeser1 05:01, 27 July 2007 (UTC)
replies: text: OK, I did the move. Oleg Alexandrov (talk) 02:05, 24 August 2007 (UTC)
thread_title:  "Thomae's function" vs "popcorn function" 

message: I uploaded a newer version with a higher resolution (:Image:Popcorn function plot bars.png, even a SVG version up to denomiator 750 (:Image:Popcorn function plot bars.svg), but this is not working at the moment, see commons:Commons:Help_desk#SVG_too_big.2C_.svg.gz__or_.svgz_was_not_accepted. What do you think? --84.72.190.27 (talk) 10:01, 27 November 2007 (UTC)
thread_title:  Newer image with higher resolution 

message: In God Created the Integers, Stephen Hawking refers to what is defined here as the Dirichlet function as the "characteristic function of the rationals in the reals", and instead calls this function the "Dirichlet function".  Wolfram MathWorld defines both of them under the same banner "Dirichlet function", where the function may take the two values (for rational and irrational) as additional parameters; it calls this function the "modified Dirichlet".
I remain uncertain that either "Thomae's function" or "popcorn function" is a proper canonical name if it is not the most common name in the literature.  At the very least it should be mentioned that this function is quite often called "the Dirichlet function", regardless as to its attribution (which is correctly given to Thomae).  TricksterWolf (talk) 00:42, 26 August 2011 (UTC)
thread_title:  Naming convention? 

message: I tweaked the lede, added a few properties, and tweaked the proofs. I tried to keep the proofs as elementary epsilon/delta proofs, and also to be constructive and rigorous. Purgy (talk) 10:15, 19 September 2017 (UTC)
thread_title:  Amendments and tweaks 

message: the intro is a , excuse me, shitty cause it is not written for a general audience
a def of coprime should be given and wtf are Z and N ?
you math people in general do a really bad job at writing stuff for general audiences - not just this article  — Preceding unsigned comment added by 73.119.28.38 (talk) 12:22, 31 May 2019 (UTC)
thread_title: the level is not right for a general encylopedia

message: Do you guys think we should include the fact that the reciprocal of the function (mapping the irrationals to 1 instead of 0) takes on every real value on every interval?
Joel Brennan (talk) 20:20, 13 April 2018 (UTC)
replies: text: Neither I am sure about your meaning of "reciprocal", nor do I understand the "every real value on every interval" (e.g., I see no negative reals anywhere.) Please, express your idea more consistently. Purgy (talk) 06:39, 14 April 2018 (UTC)
replies: text:  I mean \frac{1}{\tilde{f}} where \tilde{f} is the same as f except that in the second piece we map to 1 instead of 0. You could achieve the same effect (and I think it would be nicer) if you took the reciprocal of the first piece of f and left the second piece alone. And of course you are right; the reciprocal function only takes on the positive (or non-negative if you leave the second piece alone) real values on every (non-degenerate) real interval. Joel Brennan (talk) 13:10, 15 April 2018 (UTC)
replies: text:  I am still not sure about your intentions, but -as I currently interpret your text- "your reciprocal function" would have only natural numbers as values (q is natural, 1/q is rational, and 1/(1/q) is natural again, 1 and 1/1 and 1/(1/1) are also natural). Please, carefully rethink your considerations. Purgy (talk) 13:52, 15 April 2018 (UTC)
replies: text: Yes I'm being an idiot! It is only unbounded on every interval. That makes my supposedly 'interesting property' much less noteworthy, so it probably isn't worth remarking on in the main article. Joel Brennan (talk) 17:29, 15 April 2018 (UTC)
thread_title:  Reciprocal of the popcorn function