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What is an infimum?

What is an infimum? Here are some definitions.

Noun
  1. (mathematics) (of a subset) the greatest element of the containing set that is smaller than or equal to all elements of the subset. The infimum may or may not be a member of the subset.
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To ensure nondecreasing lower bounds, the hyper-rectangle to be bisected is chosen by selecting the region which contains the infimum of the minima of lower bounds.
Just as we proved that the supremum is unique, one can also show that the infimum is unique.
If it is infinite, this property implies another kind of convergence: all the configurations reachable from two given configurations are reachable from their infimum.

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