>>13890439This basically means your function has no "breaks" in it.
You can pick ANY Epsilon (for example 0.0000000001) and will always find some according value Delta so that if you add or remove that Delta to any of the x values, the result will be in the interval y to y+Epsilon (or y-Epsilon).
What would be an exception?
If you had a "break" in this function somewhere (i.e. a step function like Heaviside) you can set Epsilon = 0.2. At the point x=0 you can NOT find any Delta, so that f(x +/- Delta) is smaller than the chosen Epsilon (0.2).
Matter of fact any value Delta - no matter how small - will result in a difference Epsilon that is 1 - because the Heaviside does a step of 1 at the point x=0.
Since an Epsilon exists where you can't find a Delta that makes the term "work", you already know you have a "break" in it.
