## What Does mathematical limits Mean

The term that we are now going to analyze is interesting to note 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 limitis that can be translated as edge or border of something.

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

The idea of a mathematical limit has different uses.

What is a limit

The division that marks a separation between two regions is known as the boundary . This term is also used to name a restriction or limitation, to the extreme that can be reached from the physical aspect and to the extreme that a temporary period reaches.

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

The notion of mathematical limit

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

However, in addition to the aforementioned limit, we cannot ignore that there are other very important ones in the field of Mathematics. Thus, it is also possible to speak of the limit of a sequence that can be existing or unique and divergent, in the event that its terms do not converge at any point.

Mathematical limits are associated with functions.

In the same way, we must also speak of 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, named after the Polish mathematician Stefan Banach, is the one that revolves around what is known as the Banach space. This is a fundamental piece within what is functional analysis and can be defined as the space where there are functions that have an infinite dimension.

Usefulness of the concept

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

In mathematics, as we have already seen, the notion is linked to the variation of the values that functions or sequences take and to the idea of approximation between numbers . This tool helps to study the behavior of the function or the sequence 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 calculus .