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The "FS2/Theory" page has been changed by brane: http://wiki.apache.org/subversion/FS2/Theory?action=diff&rev1=6&rev2=7 applied to the binary-digit sequence representation of data configurations. It is easy to show⚑ 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 is 1. - * The maximum distance between any two distinct configurations is the greater of their sizes: ∀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: ∀a,b ∈ 𝔹: 𝓁(a, b) ≤ max(''S'',,a,,, ''S'',,b,,); - * from wich it follows that: ∀c ∈ 𝔹: 𝓁(𝑒, c) = ''S'',,c,,. + * from wich it follows that: ∀c ∈ 𝔹: 𝓁(𝑒, c) = ''S'',,c,,. + * All distances are non-negative integers. In the rest of this text, we'll specifically talk about (𝔹, 𝓁) — that is, the data configuration space with a Levenshtein distance metric; also referred to as ''[[http://en.wikipedia.org/wiki/Edit_distance|edit distance]]''. Even though the term "edit distance" is less precise in general, it fits the concept of ''edits'' (or ''edit transformations''), which we'll discuss later on.
