# Talk:Minkowski's question-mark function

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## About the derivatives

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)

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