What is continuity at a point?

1 Answer
Jun 8, 2018

Let f(x)f(x) be a real function of real variable defined in the domain I sub RR.

Let x_0 in I be a point of accumulation for I.

The function f(x) is continuous in x_0 if:

lim_(x->x_0) f(x) = f(x_0)

that is if the limit of f(x) as x approaches x_0 equals the value of the function in x_0. This means that as x gets closer and closer to x_0, then f(x) gets closer and closer to f(x_0), so that the graph of the function has no "jumps".