[Math] What does this sentence mean? “$\lim_{x\to x_0}$ exists at every point $x_0$ in $(-1,1)$.”

Question

What does this sentence mean?
$$\lim_{x\to x_0} \;\text{exists at every point}\; x_0 \; \text{in} \; (-1,1).$$

$(1,-1)$ is just an example point. The topic is finding whether limit functions are true or false and this is one of the questions.

Answer 1

For every $x_0$ inside of the interval $(-1,1)$, meaning all points bigger than $-1$ but less than $1$, not including those two numbers, the limit of the function as $x\rightarrow x_0$ neither blows up, nor does it oscillate, it approaches some finite value.