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Lecture# Real Analysis: Functions and Limits

Description

This lecture covers the basics of real analysis, including functions, limits, real numbers, sequences, and max/min functions. It explains the concept of limits at a point, maximum, minimum, supremum, and infimum. The lecture also discusses periodicity and parity in functions.

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Étudier les concepts fondamentaux d'analyse et le calcul différentiel et intégral des fonctions réelles d'une variable.

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Limit inferior and limit superior

In mathematics, the limit inferior and limit superior of a sequence can be thought of as limiting (that is, eventual and extreme) bounds on the sequence. They can be thought of in a similar fashion for a function (see limit of a function). For a set, they are the infimum and supremum of the set's limit points, respectively. In general, when there are multiple objects around which a sequence, function, or set accumulates, the inferior and superior limits extract the smallest and largest of them; the type of object and the measure of size is context-dependent, but the notion of extreme limits is invariant.

Infimum and supremum

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