Math and science::Analysis::Tao::09. Continuous functions on R

Left and right limits

The two separate halves of a complete limit $lim_{x \to x_{0}; x \in X} f (x)$ .

Let $X$ be a subset of $R$ , $f : X \to R$ be a function and $x_{0}$ be a real number.

If $x_{0}$ is an adherent point of [...], then we define the left limit, $f (x_{0} -)$ of $f$ at $x_{0}$ to be:

[...]

If $x_{0}$ is an adherent point of [...], then we define the right limit, $f (x_{0} +)$ of $f$ to be:

[...]

Note: if and only if $x_{0}$ is an adherent point of $(- \infty, x_{0})$ then it is a limit point of $(- \infty, x_{0}]$ , as adherent to a set minus the element in question is the definition of being a limit point of that set.

16.03.2020