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Let **<=** be a total order on an alphabet `A`,
let `W`_{n} := **N**_{n} -> `A` be the set of all words with `n` letters, and let

:=wsuchu:existsninN:winW_{n}/\uinW_{n-1}/\foralliinN_{n-1}:u_{i}=w_{i+1}

The *lexicographic order* **<=** _{n}
subset `W`_{n} x `W`_{n} defined as

is a total order.

w<=_{n}u: <=>n= 0 \/w_{0}<u_{0}\/ (w_{0}=u_{0}/\w<=_{n-1})u

"back"<_{4}"bare"<_{4}"base"<_{4}"bear"<_{4}"bend"<_{4}"care"

*Compare letters in the order of their positions.*

Author: Wolfgang Schreiner

Last Modification: January 18, 2000