# Talk:Minkowski's question-mark function

WikiProject Systems (Rated Start-class, Mid-importance)
Start  This article has been rated as Start-Class on the project's quality scale.
Mid  This article has been rated as Mid-importance on the project's importance scale.

It does not have a well-defined derivative, in the classical sense, on the irrationals;

That's impossible! Any monotonic function has a derivative almost everywhere. --a_dergachev (talk) 03:50, 8 May 2009 (UTC)

You are absolutely correct. (See Monotonic function for example. I am not surewhat the intended statement is but I am deleting the formulation as it is now since it is clearly wrong. I am also deleting another confusing statement
The derivative vanishes on the rational numbers; however, since the rationals are a set of measure zero,
this vanishing of the derivative at the rationals is not in contradiction with the non-absolute continuity of the function.
There are non-absolutely continuous functions with derivatives that vanish almost everywhere (the Cantor function for example) making this statement incomprehensible.(Sorry about the confusing mark-up of my post.) --MathHisSci (talk) 12:43, 18 March 2010 (UTC)

Just a comment, this has to be the worst example of bad choice of notation...what was he thinking?? Revolver 07:06, 21 May 2005 (UTC)

Dates back to the dawn of the discovery of pathological functions, at the turn of the 20th century. Maybe it was felt to be very confusing? And maybe he had a twisted sense of humour. linas 00:36, 22 May 2005 (UTC)

## Mathematica implementation/hack

In case anyone looks for a short Mathematica one-liner implementing ?(x) for numerical values (I guess that would mean: for rationals) :

qm[x_] := Abs@Fold[#2 - #1 &, Floor@x, 2*2^-Accumulate@Rest@ContinuedFraction@x]

Summsumm2 (talk) 16:08, 4 February 2013 (UTC)

## Conway box function and Sawtooth wave question

The Conway box function section says See also: Sawtooth wave, but neither mentions the other one. What is the connection? How reading about Sawtooth wave allows better or deeper understanding of a boxed question mark function? --CiaPan (talk) 10:22, 22 April 2015 (UTC)

I also did not see the link. I suggest this link be deleted. Also, reading the book of Conway it looks like his function is actually Minkowski's question mark, and not its inverse bijection (figure 8, page 84 there). Saros (talk) 22:26, 3 December 2017 (UTC)

## A box

I could not find a single LaTeX command for a box to surround a given expression, however discovered a quite simple way do make a box with an array:

\begin{array}{|c|} \hline EXPR \\ \hline \end{array}

Result:

${\displaystyle {\begin{array}{|c|}\hline EXPR\\\hline \end{array}}}$

The {|c|} part declares a single column in the array with centered contents and vertical lines on both sides. Commands \hline add horizontal lines above and below the (single) row. Command \\ terminates the row so that the bottom line can be drawn.
Happy editing, everybody! :) CiaPan (talk) 10:50, 22 April 2015 (UTC)

## Salem's problem

There were two solutions posted on Salem's problem during Jan 2015. One was a special case of an earlier result by Jordan and Sahlsten (arXiv:1312.3619), that was submitted to arXiv on December 12, 2013 and accepted to the journal Mathematische Annalen on February, 2015, according to the arXiv version from February 2015. The earlier version of the paper by Jordan and Sahlsten did not mention Salem's problem and the application was pointed out by Persson (arXiv:1501.00876) in a note from January 5, 2015. Yakubovitch's answer (arXiv:1501.00141) was submitted to arXiv on December 31, 2014, and the corrected revision of that article was posted to arXiv on April 15, 2015. — Preceding unsigned comment added by 79.176.37.159 (talk) 06:45, 13 May 2015 (UTC)

Hello fellow Wikipedians,

I have just modified 2 external links on Minkowski's question-mark function. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:

When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.

You may set the |checked=, on this template, to true or failed to let other editors know you reviewed the change. If you find any errors, please use the tools below to fix them or call an editor by setting |needhelp= to your help request.

• If you have discovered URLs which were erroneously considered dead by the bot, you can report them with this tool.
• If you found an error with any archives or the URLs themselves, you can fix them with this tool.

If you are unable to use these tools, you may set |needhelp=<your help request> on this template to request help from an experienced user. Please include details about your problem, to help other editors.

Cheers.—InternetArchiveBot 09:54, 27 December 2017 (UTC)