The notion of convergence (in any manner) has many useful applications involve real-life problems. This concept plays an important role in the solution of various equations such as algebraic, differential, integral, etc.There are many different types of convergence such as statistical convergence, convergence of a series, modular convergence, convergence of a continued fraction, convergence of an integral etc.
My question is: can it be possible to find any natural concept closely related to the convergence of a sequence (in any manner) in real life. What is the counterpart of epsilon, n, n_0 in real life (if there exist)? Formally x_n--->x, if, for any epsilon >0, there exist an n_0 such that |x_n-x|n_0. I mean that,
Let each term of sequence x_n be represented by a person.
Suppose that x represents the true love or honesty.
What is the best way to find true love (or to be honest) in mathematical sense?
Dear Breuer,
I dont agree with you. Of course, the convergence is closely related to the concept of "limit". It is very clear. At this stage, there is no need any explanations, especially using inappropriate words. Here, I investigate some equivalent terms (in reall life) for the epsilon, n and n_0. What is the meaning of epsilon and n_0 in real life (if there is)? In my opinion, we can find suitable concepts in real life with respect to it. Really, I'm looking for an approach like this not the meaning of the limit of sequence. Which concept (in reall ife) is based on the specific term n_0 of sequence, or the number epsilon which represents arbitrarily small neighborhood of the limit.
Dear Breuer,
Thanks for examples but these are well known. Even if I do not like your some words above (grade school etc.), I feel the need to make an explanation. In my opinion, we can find suitable concepts in real life with respect to these notions. For example,
Suppose that each terms of a sequence represents the individuals who make up society. Suppose also that the limit of the sequence is democracy. That is, the ultimate goal is to become a democratic society. In such societies, a certain majority (except many indivudials) must be in any neighborhood of democracy. Of course, this concept may be different for every society. As you know, some common values have been accepted for the concept of democracy. For this reason, the epsilon may be represented as these neighborhoods. Also, the number n_0 can be represented this certain majority (or number). I am interested in such examples. Even if it is at grade school level for you, I am looking for examples of this type. Thank you.
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