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Baris 163: If < is a total order on ''A'', then so is the lexicographic order <<sup>d</sup> on ''A''. If ''A'' is a finite and totally ordered alphabet, ''A'' is the set of all [[String (computer science)#Formal theory\|words]] over ''A'', and we retrieve the notion of dictionary ordering used in lexicography that gave its name to the lexicographic orderings. However, in general this is not a [[well-order]], even though it is on the alphabet ''A''; for instance, if ''A'' = {''a'', ''b''}, the [[Formal language\|language]] {''a''<sup>''n''</sup>''b'' \| ''n'' ≥ 0} has no least element: ... <<sup>d</sup> ''aab'' <<sup>d</sup> ''ab'' <<sup>d</sup> ''b''. A well-order for strings, based on the lexicographical order, is the [[shortlex order]]. Similarly we can also compare a finite and an infinite string, or two infinite strings. Baris 191: and also to look at higher terms first, that means ordering : ... < ''X''<sup>3</sup> < ''X''<sup>2</sup> < ''X'' and also

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