The smallest element with an upper bound is called the minimum upper bound; The largest element of the lower bound is called the maximum lower bound; Just like this picture, if you want to find the minimum upper bound on B and D, you must find the upper bound on B and D, and the only upper bound on B and D is F.

The smallest element in the upper bound can only be f; If you look for the maximum lower bound of de, the lower bound of de is abc, and then you look for the maximum element in abc, because abc has no maximum element, so there is no maximum lower bound.

Extended data:

In the general textbook of mathematical analysis, in the chapter of real number theory, there are a series of theorems to illustrate the compactness of real numbers. Textbooks of the former Soviet Union with rigorous theory are generally based on Dydykin's division theorem to prove other equivalence theorems. In order to simplify textbooks in China, many of them are proved from the perspective of clear definition;

Other theorems that illustrate the continuity of real numbers include interval set theorem, finite covering theorem and so on. Definite theorem is one of the most basic conclusions in real number theory and the embodiment of the compactness of real number set. Theorem: Any set of non-empty real numbers with upper bound (lower bound) must have upper supremum (lower supremum).

"Lower supremum" is a basic concept in mathematical analysis, which is defined on the basis of "lower bound". Given a set of numbers e, we call the maximum lower bound of e the lower supremum of e, and we call it infE. Obviously, every element in E is greater than or equal to infE.

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