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The "FS2/Theory" page has been changed by brane: http://wiki.apache.org/subversion/FS2/Theory?action=diff&rev1=2&rev2=3 ''N.B.'': Although the following text uses mathematical concepts and notation, it's not intended to be a rigorous dissertation on configuration theory. We'll often make statements and draw conclusions without providing proof. Therefore, dear reader, you can either trust we're right, or do your own homework to prove (or disprove) our assertions. We will, however, try to conscientiously flagβ all leaps of faith in the text. '''Definition:''' A ''data configuration'' is a unique pattern of data that can be represented as exactly one distinct sequence of binary digits. - * The representation of the ''empty configuration'' {} is the zero-length sequence. + * The representation of the ''empty configuration'' π is the zero-length sequence. - * The ''size'' , βcβ, of a configuration c is the length of its representative sequence of binary digits. + * The ''size'' , ''S'',,c,,, of a configuration c is the length of its representative sequence of binary digits. '''Definition:''' A ''data configuration space'' is a [[http://en.wikipedia.org/wiki/Metric_space|metric space]] (πΉ, πΉ) where: * πΉ is the set of all data configurations; @@ -24, +24 @@ applied to the binary-digit sequence representation of data configurations. It is easy to showβ that π has all the required properties of a metric. In addition, it has the following properties: * The minimum distance between any two distinct configurations isβ 1. - * The maximum distance between any two distinct configurations isβ the greater of their sizes: βa,b β πΉ: π(a, b) β€ max(βaβ, βbβ) . + * The maximum distance between any two distinct configurations isβ the greater of their sizes: βa,b β πΉ: π(a, b) β€ max(''S'',,a,,, ''S'',,b,,) . - * And it followsβ from this that: βc β πΉ: π({}, c) = βcβ . + * And it follows from this that: βc β πΉ: π(π, c) = ''S'',,c,, .
