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Definition: For every variable n and terms S and T, the phrase
S = On(T)is a proposition with bound variable n which is read as "S is big O of T" or "T asymptotically dominates S".
Its meaning is equivalent to the proposition
exists c in R, m in N: forall n >= m: |S| <= c*|T|.
Usually the subscript n is dropped and the bound variable has to be deduced from the context.