In some case, there is no easy way to tell without just directly checking the definition. The piecewise function f (0)=1, f (x)=sin (x)/x for x nonzero is continuous, but it's not obvious that it
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In plain English, a real function f is continuous if you can draw its graph without lifting your pen. Id est, if the set of points {(x,f(x))} is a path-connected set. (This is a little circular since you need
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