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Mathematical Limits

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The term that we are going to analyze now is interesting to emphasize that it is formed by the union of two words that have their etymological origin in ancient languages. Thus, limits comes from the Latin word limes, which is the genitive of limit which can be translated as border or border of something.

On the other hand, mathematicians is a word that has its origin cited in the Greek and specifically in the term mathema. This can be defined as the study of a particular topic or issue.

The division which marks a separation between two regions is known as limit . This term is also used to name a restriction or limitation, to the extent that can be reached from the physical aspect and to the point at which a time period arrives.

For the math , a limit is a magnitude to which the terms of an infinite sequence of magnitudes progressively approach. A mathematical limit , therefore, it expresses the tendency of a function or a sequence as its parameters approach a certain value.

An informal definition of the mathematical limit indicates that the limit of a function f (x) is T when x tends to s , provided that you can find for each occasion a x near s so that the value of f (x) be so close to T as intended.

However, in addition to the quoted limit, we cannot ignore that there are others that are very important in the field of Mathematics. Thus, we can also talk about the limit of a sequence that can be existing or unique and divergent, in the event that the terms of that sequence do not converge at any point.

In the same way, we must also talk about another series of mathematical limits such as the limit of a succession of sets or that of topological spaces. Among the latter are those that refer to filters or networks.

Finally, we cannot ignore the existence of what is known as the Banach Limit. The latter, which is called the Polish mathematician Stefan Banach, is the one that revolves around what is known as Banach space. This is a fundamental piece of what functional analysis is and can be defined as the space where there are functions that have an infinite dimension.

Like other mathematical concepts, the limits meet various general properties that help simplify the calculations . However, it can be very difficult to understand this idea since it is an abstract concept.

In mathematics, the notion is linked to the variation of values that take the functions or sequences and with the idea of ​​approximation between numbers . This tool helps to study the behavior of the function or succession when they approach a given point.

The formal definition of the mathematical limit was developed by various theorists around the world over the years, with works that formed the basis of the Infinitesimal calculation .

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