Why should the definition of function limit be de centered?

Why should the definition of function limit be de centered?

A function does not necessarily have a definition at that point, so it is stipulated that it is the centreless critical region of a, that is, that point is dispensable for the function limit. Therefore, even if the function has a definition at that point, we will dig out that point, and it will not affect the limit value, so it is convenient for us to discuss the limit (because it unifies the limit of the function with and without definition at that point into one form: a) To the heart of the pro domain

Why is the definition of function limit always a point to the heart of the neighborhood? Why to the heart?

Limit is just a trend, because x → XO and X →∞ are two processes. X → XO indicates that x is infinitely close to XO, but not equal. In "let function f (x) have a definition in a centroid neighborhood of point XO", 1. It reflects x → XO, but not equal; 2. It makes the definition of limit more extensive, that is

What kind of function has limit? Is the domain of definition r of the function with limit

If the graph of a function is a smooth curve, the domain of a function with a limit does not necessarily belong to R

What does "neighborhood" mean in function limit?

Neighborhood
Any open interval centered on a is called the neighborhood of point a, denoted as u (a)
Let δ be any positive number, then in the open interval (a - δ, a + δ) is a neighborhood of point a, which is called the δ neighborhood of point a, denoted as u (a, δ), that is, u (a, δ) = {x | a - δ

Is the neighborhood of a function for the limit? Is there a definition in a centreless neighborhood of a? Is it that the independent variable can't get a when seeking the limit, or is there no definition in a

If the independent variable cannot get a, it may not be undefined

The basic knowledge of a neighborhood in Higher Mathematics
Let a, δ, (a - δ, a + δ) be a neighborhood of a, denoted as: {x | a - δ

No, X is a range, greater than one value, less than one value, a - δ

Let a and B be two real numbers, and b > 0. Call the number set B neighborhood of point a, u (a, b). Point a is called neighborhood center, and point B is called neighborhood radius,

In fact, neighborhood means a limit interval. It is represented by a very small interval (A-B, a + b) as the neighborhood of point A. some concepts can only be used in this interval. B can be regarded as an infinitesimal. When we are seeking the limit of a point or whether a function is continuous at a certain point

What is the neighborhood of high number

Any open interval centered on a is called the neighborhood of point a, denoted as u (a) neighborhood
Let δ be any positive number, then the open interval (a - δ, a + δ) is a neighborhood of point a, which is called the δ neighborhood of point a
δ (a) = {a + U}

What does neighborhood mean in high numbers

The neighborhood of a point in high number is a region centered on the point, and the size of the region is determined by the problem
One is the neighborhood of a point on the number axis, and the other is the neighborhood of a point on the plane
For example, a is a point on the number axis, and the ε neighborhood of a is (a - ε, a + ε). A (x, y) is a point on the XY plane, and the ε neighborhood of a is a circle with a (x, y) as the center and ε as the radius
It should be emphasized that ε must be a positive number and ε ≠ 0, that is, ε > 0. The size of neighborhood is determined by the size of ε

I don't understand one of the lobita's rules in higher mathematics, which is called "heartless neighborhood". What is "heartless neighborhood"?

Let a be any real number, that is, a point on the number axis. Any open interval with a as the center is called a field of point a, denoted as u (a). The set obtained by removing a from u (a) is denoted as u (a), that is, u (a) = u (a) - ∣ a ∣ which is called the centreless neighborhood of A