I would like to construct a diagram which is a variation of the middle third Cantor set as described by:  Suppose we start off with the unit interval $[0,1]$; let us call it $A_0$. Next, remove the segment $(1/4,3/4)$ and then repeat the process on the two intervals $[0,1,4]$ and $[3/4,1]$ which make up $A_1$. In doing so we obtain $A_2=[0,1]\setminus \{ (1/16,3/16)\cup(13/16,15/16) \}$. We define the set $A$ by repeating process ad infinitum and so $A= \cap_{k=0}^{\infty} A_k$.  I would like this diagram to look something like this (my middle third Cantor diagram):    I do not know nothing anything about constructing these diagrams.
I am trying to draw a cantor set in LaTeX and I am having issues doing this. I am trying multiple \put commands, but they just go to the right of one another. Does anyone know how to do this?  Any help would be much appreciated.
Wall of Sand on Difficult Terrain Looking into  prompted this inquiry:  What happens when you move through a wall of sand on difficult terrain?  This involves the understanding that wall of sand changes the cost of moving 1 foot to 3 feet and that difficult terrain typically changes the cost of moving 1 foot to 2 feet. Is "this Monday" or "next Monday" the correct way to refer to the very next Monday in the future? Possible Duplicate:          When I refer to the very next Monday that will occur in the future, I say "next Monday". Some colleagues refer to it as "this Monday", with "next Monday" meaning the second Monday which will occur in the future (I would refer to that as "Monday week", "this Monday" to me would mean the most recent Monday in the past).  Are these both acceptable usages, or is one more correct than the other? So,  Each of my polygons is a separate object. 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Quite often I need to perform this two commands:  mkdir abc cd abc   I am curious whether there is a simple command (or an alias that I can create and use) to do it in one go, like  user@GROUP:~$ mdcd abc user@GROUP:~/abc$   Is this possible? Floating sidebar can get too long and obscure footer Why are Marketing Cloud timestamps not stored in the same timezone as Sales Cloud? How to use \def to redefine \end{split}? When I use \def to redefine \end{split}, there is an error.  \documentclass{article} \usepackage{amsmath}  \begin{document} \def\be{\begin{equation}} \def\ee{\end{equation}} \def\bs{\begin{split}} \def\es{\end{split}}  \be     \bs         a\\         b     \es \ee  \end{document}   The error is:      Runaway argument?      a\ b \es \ee       ! Paragraph ended before \split was complete.   However, if I don't use \def\es{\end{split}} and just modify the code to be  \documentclass{article} \usepackage{amsmath}  \begin{document} \def\be{\begin{equation}} \def\ee{\end{equation}} \def\bs{\begin{split}} \def\es{\end{split}}  \be     \bs         a\\         b     \end{split} \ee  \end{document}   it's OK. What's the problem? Thank you! Is it a problem if a UK visa was issued but not used? Last year, my wife and I were issused 6-month visieor visas for the UK. She did not travel with me and, therefore, didn't use her visa. I am currently applying for a visitor visa for my daughter and myself.  Will the fact that my didn't use her visa have any negative affect on our new application? Prove $(x_1+.....+x_n)^2 \leq n(x_1^2 + .....+x_n^2)$ Prove that  $(x_1+\dots+x_n)^2 \leq n(x_1^2 + \dots+x_n^2)$  for all positive integers n and all real numbers $x_1,....,x_n$  I am attempting a proof by induction but wasn't sure if i need the Cauchy-Schwarz Inequality or perhaps another way other than induction to prove this.  Proof   $n=1$ true  assume true for $n=k$  Now for $n= k+1$  $(x_1 + \dots +x_k + x_{k+1})^2 \leq \dots$