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Sequences

Definition: sequence of length n over S

s is a sequence of length n over S : <=> s: N_n -> S.

Definition: length of a sequence

length(s) :=
   such n in N: exists S: s is a sequence of length n over S.

Definition: finite sequence

s is a finite sequence over S : <=>
   exists n in N: s is a sequence of length n over S.

Definition: infinite sequence

s is an infinite sequence over S : <=> s: N -> S.