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Definition: Let f be an infinite sequence over R. f is monotonically increasing if every element of f is less than or equal the next element:
f is monotonically increasing : <=> f: N -> R /\ forall i in N: fi <= fi+1.
f is strictly monotonically increasing if every element of f is less than the next element:
f is strictly monotonically increasing : <=> f: N -> R /\ forall i in N: fi < fi+1.