Révision 193

CSL17/ph-macros.tex (revision 193)
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\newcommand{\pair}[3]{\langle ; #1,#2 , #3 \rangle}
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\newcommand{\eq}{\textsc{eq}}
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\newcommand{\leqfn}{\textsc{leq}}
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\newcommand{\bit}{\textsc{Bit}}
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\newcommand{\safe}{{N_0}}


  		












  

    
      CSL17/sequence-coding.tex	(revision 193)
    
  






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For an arbitrary sequence we cannot use quite the same technique since length is not determined in advance. 


  		





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However, by using a slightly more asymmetric encoding we can still access all required bits in quadratic modulus rather than linear, appealing to a `zig-zag' technique.


  		





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\anupam{Every number is an infinite ultimately 0 sequence.}


  		





  
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\anupam{Every number is an infinite ultimately 0 sequence.}


  		





  
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\begin{definition}


  		





  
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[Sequence (de)coding]


  		





  
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We define the function $\beta\bit (i,j;x,b)$, intuitively meaning ``the $j$th bit of the $i$th element of $x$ is $b$'' as $\bit \left( \frac{1}{2} (i+j)(i+j+1) +i ; x , b \right)$.	


  		





  
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\end{definition}


  		












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