I’m looking at the definition and can’t wrap my head around
In: Mathematics
In simple terms: if x and y are very close, then f(x) and f(y) must also be very close for a uniformly continous f.
There exists a distance between x and y that brings the difference between f(x) and f(y) below some arbitrary limit epsilon (as small as we want)
In practise that means that the function has no infinite values, and no infinite slopes anywhere.
Typical counterexamples are 1/x (infinite value and slope at values close to 0) and the heavyside function (infinite slope at 0, if x is positive and y is negative then no matter how close you put them the difference between f(x) and f(y) is always 1 so we can’t make it as small as we want)
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