inf means "infimum," or "greatest lower bound." This is slightly different from minimum in that the greatest lower bound is defined as: x is the infimum of the set S [in symbols, x = inf (S)] iff: a) x is less than or equal to all elements of S b) there is no other number larger than x which is less than or equal to all elements of S. Basically, (a) means that x is a lower bound of S, and (b) means that x is greater than all other lower bounds of S.
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