Question is basically just what is in the title. I am trying to prove that the function $f\colon [0,1] \to \mathbf R$ being not continuous implies that the function is not regulated over the interval $[0,1]$. This is an undergrad analysis course question.
For those unfamiliar with the notion of 'regulated', it means that a left and right limit exists at each $x \in [0,1]$ in this case.
The original q is asking to show that the above function is continuous IFF it is regulated. I have shown cont => regulated but I’m struggling to show reg => cont, so I’m trying the contrapositive (hence the question).
Thank you!