Maximum and minimum in the context of "Supremum"

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⭐ Core Definition: Maximum and minimum

In mathematical analysis, the maximum and minimum of a function are, respectively, the greatest and least value taken by the function. Known generically as extrema, they may be defined either within a given range (the local or relative extrema) or on the entire domain (the global or absolute extrema) of a function. Pierre de Fermat was one of the first mathematicians to propose a general technique, adequality, for finding the maxima and minima of functions.

As defined in set theory, the maximum and minimum of a set are the greatest and least elements in the set, respectively. Unbounded infinite sets, such as the set of real numbers, have no minimum or maximum.

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👉 Maximum and minimum in the context of Supremum

The infimum is, in a precise sense, dual to the concept of a supremum. Infima and suprema of real numbers are common special cases that are important in analysis, and especially in Lebesgue integration. However, the general definitions remain valid in the more abstract setting of order theory where arbitrary partially ordered sets are considered.

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Maximum and minimum in the context of Apogee

An apsis (from Ancient Greek ἁψίς (hapsís) 'arch, vault' (third declension); pl.apsides /ˈæpsɪˌdz/ AP-sih-deez) is the farthest or nearest point in the orbit of a planetary body about its primary body. The line of apsides (also called apse line, or major axis of the orbit) is the line connecting the two extreme values.

Apsides pertaining to orbits around different bodies have distinct names to differentiate themselves from other apsides. Apsides pertaining to geocentric orbits, orbits around the Earth, are at the farthest point called the apogee, and at the nearest point the perigee, as with orbits of satellites and the Moon around Earth. Apsides pertaining to orbits around the Sun are named aphelion for the farthest and perihelion for the nearest point in a heliocentric orbit. Earth's two apsides are the farthest point, aphelion, and the nearest point, perihelion, of its orbit around the host Sun. The terms aphelion and perihelion apply in the same way to the orbits of Jupiter and the other planets, the comets, and the asteroids of the Solar System.

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