Minimum

The minimum is the smallest or least quantity that is possible or necessary. You will not be fired if you do the bare minimum of work at your job, but you will not be promoted.

Since minimum is Latin for smallest, English speakers have obviously done the least amount of interfering with the sense of this term. Obviously, the opposite is Maximum. At the minimum, you should understand that the term refers to something's smallest limit.

Meaning of Min (Minimum)

In a given set of data, the smallest or the least number is said to be the minimum number. It can be easily detected by arranging the given data in descending or ascending order. For example, the given series of numbers is 167, 897, 69, 301, 999, 294. If we arrange this series in descending order we will get 999, 897, 301, 294, 167, 69. Thus, this clearly shows 69 is the minimum number which got its place at the end.

Minimum in Mathematics

The maxima & minima (the plurals of maximum and minimum) of the function, known collectively as extrema (the plural of extremum), are the function's largest and smallest values, either within a given range (the local or relative extrema) or on the entire domain (the global or absolute extrema). Pierre de Fermat was one of the first mathematicians to introduce a general technique for determining the maxima and minima of functions, known as adequality.

The maximum and minimum of a set are the greatest and least elements in the set, as defined by set theory. There is no minimum or limit for unbounded infinite sets, such as the set of real numbers.

Maxima or Minima of a Function

When the domain of a function in which an extremum is to be found is made up entirely of functions (i.e. if the extremum of a function is to be found), the extremum is found using the calculus of variations.

A maximum is a term used to describe a high point (plural maxima). A minimum is a term used to describe a low point (plural minima). Extremum is a general term for maximum or minimum (plural extrema). When there are higher (or lower) points elsewhere but not nearby, we say local maximum (or minimum).

In Relation to Sets

Sets may also have maxima and minima specified. If an ordered set S has the greatest element m, then m is the set's maximum element, also known as max (S). In addition, if S is a subset of an ordered set T and m is the greatest element of S with (respect to the order induced by T), then m is the least upper bound of S in T. The least element, minimal element, and greatest lower bound all yield similar results. Since the maximum (or minimum) of a set can be computed from the maxima of a partition, the maximum (or minimum) of a set can be computed quickly in databases; formally, they are self-decomposable aggregation functions.

Absolute Minimum and Maximum

An absolute maximum point is a point at which the function achieves its maximum value. An absolute minimum point, on the other hand, is the point at which the function takes on its smallest possible value.

If you already know how to locate relative minima and maxima, you'll need to consider the ends in both directions to find absolute extrema points.

Conclusion

At the minimum, you should be able to understand that the smallest number is said to be the minimum number. A maximum is a term used to describe a high point (plural maxima). A minimum is the smallest or least quantity that is possible or necessary. In mathematics, if an ordered set S has the greatest element m, then m is the set's maximum element, also known as max (S) absolute maximum points are self-decomposable aggregation functions. An absolute minimum point is a point at which the function achieves its maximum value. If you already know how to locate relative minima and maxima, you'll need to consider the ends in both.