# Confusing regarding triangular wave vs square wave?

I am reading signal processing first by Mcclellan. In chapter 3, I came across the term "discontinous" as shown underlined in attached photo.

Apparently "discontinuous" means having a gap/break but in attached photo we see square wave is mentioned as discontinuous while triangular wave is mentioned as continuous, although there isn't any apparent gap/break in both graphs.

What is the reason for this difference? In context of dsp?

• as said below your last quesion on "discontinuous signals", the term is mathematically well-defined, and I linked to that definition. I'm not really sure what this near-identical question is about now. – Marcus Müller Apr 3 '20 at 17:35

In other words, a function that is defined like this: $$f(t) = \begin{cases} 0\,\,\,t<0\\1\,\,\,t>=0\end{cases}$$ is discontinuous. Even if you draw a vertical line from 0 to 1 at $$t=0$$, the vertical line does not actually represent the function: $$f(t)$$ is never 0.5, or 0.3, or anything besides 0 and 1. Mathematically, the function has a different value when $$t$$ approaches 0 from the left ($$t$$ increasing from $$-\infty$$ to 0) than when approached from the right ($$t$$ decreasing from $$\infty$$ to 0).
• Any instantaneous change in amplitude implies that the spectrum extends to $\pm \infty$. – MBaz Apr 4 '20 at 18:38