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If there exists a greatest element of one set or a least element of the other set, then the cut defines a rational number; otherwise the cut defines an irrational number.
L has no greatest element.
Therefore, as, we conclude that is the greatest element in.
Moreover, let 1 denote the greatest element of Y.d.
A different choice function is obtained by assigning to each pair its greatest element.
d Note that the set Y is arbitrary, and so is its greatest element 1.
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CEO of Professional Science Editing for Scientists @ prosciediting.com