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Posted to commits@subversion.apache.org by Apache subversion Wiki <co...@subversion.apache.org> on 2012/12/01 05:48:48 UTC

[Subversion Wiki] Update of "FS2/Theory" by brane

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The "FS2/Theory" page has been changed by brane:
http://wiki.apache.org/subversion/FS2/Theory?action=diff&rev1=3&rev2=4

   * 𝔹 is the set of all data configurations;
   * 𝒹: 𝔹 Γ— 𝔹 ⟢ ℝ is a metric on 𝔹.
   
- '''Definition:''' A ''configuration history'' is a sequence of elements of the data configuration space.
+ '''Definition:''' A ''configuration history'' is a sequence of elements of the data configuration space; in other words, it is a ''curve'' in (𝔹, 𝒹).
  
  == Defining the Metric ==
  
@@ -23, +23 @@

   𝓁: 𝔹 Γ— 𝔹 ⟢ β„•^0^
  
  applied to the binary-digit sequence representation of data configurations. It is easy to showβš‘ that 𝓁 has all the required properties of a metric. In addition, it has the following properties:
-  * The minimum distance between any two distinct configurations isβš‘ 1.
+  * The minimum distance between any two distinct configurations is 1.
-  * The maximum distance between any two distinct configurations isβš‘ the greater of their sizes: βˆ€a,b ∈ 𝔹: 𝓁(a, b) ≀ max(''S'',,a,,, ''S'',,b,,) .
+  * The maximum distance between any two distinct configurations is the greater of their sizes: βˆ€a,b ∈ 𝔹: 𝓁(a, b) ≀ max(''S'',,a,,, ''S'',,b,,),
-  * And it follows from this that: βˆ€c ∈ 𝔹: 𝓁(𝑒, c) = ''S'',,c,, .
+  * from wich it follows that: βˆ€c ∈ 𝔹: 𝓁(𝑒, c) = ''S'',,c,,.
  
+ == The History Curve ==
+