Let the function y = f (x) be defined in a certain interval, where x0 and x0 + Δ X are defined. What do x0 and x0 + Δ x mean

Let the function y = f (x) be defined in a certain interval, where x0 and x0 + Δ X are defined. What do x0 and x0 + Δ x mean

X0 represents the value of the specified domain X
Δ x is any tiny increment
X0 + Δ x denotes the neighborhood of x0
In the title of analogy:
Let y = f (x) be defined in a certain interval, and x0 and x0 + Δ X be defined in this interval
The function f (x) is defined at point x 0 and its neighborhood (x 0 + Δ x)