Sup(X) is an upper bound function and inf(X) is a lower bound function.

Sup is the abbreviation of supremum, which means: supremum, minimum supremum.

Inf is the abbreviation of lower supremum, which means: lower supremum, maximum lower bound.

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First, the upper limit:

The supremum is the minimum upper bound of a set and the most basic concept in mathematical analysis. The concept of supremum is the most basic concept in mathematical analysis. Consider a set of real numbers M. If there is a real number S, so that no number in M exceeds S, then S is called an upper bound of M. ..

If there is a minimum upper bound among all those upper bounds, it is called the supremum of m?

A bounded number set has countless upper and lower bounds, but only one supremum.

Second, the lower bound:

The concept of infimum is the most basic concept in mathematical analysis. Consider a set of real numbers M. If there is a real number S that makes any number in M greater than or equal to S, then S is called a lower bound of M. ..

If there is a maximum lower bound among all these lower bounds, it is called the lower supremum of m.

A bounded number set has countless upper and lower bounds, but only one lower supremum.

Three. References and websites:

1 、/ doc/ 106 1 150- 1 122573 . html；

2 、/doc/653936-692 189.html。