Question

There is a function on the real line, r, that does not have a limit anywhere. true or false

Answer 1

It's true.

An example of such a function:

`f(x)=\begin{cases} 0 &\text{if } x \in\mathbb{Q}\\ 1&\text{if } x \\ot\in\mathbb{Q}\\ \end{cases}`