In advanced mathematics, we often use a special open interval (a -δ, a+δ), which is called the neighborhood of point A, and is denoted as U(a, δ), namely

U(a，δ) = (a - δ，a + δ)，

Call point A the center of the neighborhood and δ the radius of the neighborhood.

Usually δ is a small real number, so the δ neighborhood of A represents the neighboring point of A, as shown in the figure below.

Sometimes, we only consider the point near point A, but not point A, that is, we consider the point set {x | a-δ.

(a，δ)= { x | a-δ& lt； X<a or a < x<a+δ},

As shown in the figure below.

Any open interval centered on a is called the neighborhood of point A, and is denoted as U(a).

Let δ be an arbitrary positive number, then the open interval (a-δ, a+δ) is a neighborhood of point A, which is called δ neighborhood of point A..

Write it as u (a, δ), that is, U(a, δ) = {x | a-δ.