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Definition: Let f be an infinite sequence over R.
f has upper bound U, if every element of f is less than or equal U:
U is upper bound of f : <=> f: N -> R /\ forall i in N: fi <= U.
f has lower bound L, if every elem. of f is greater than or equal L:
L is lower bound of f : <=> f: N -> R /\ forall i in N: fi >= L.