CONTINUITY ON AN INTERVAL

f(x) IS CONTINUOUS ON AN INTERVAL,

IF IT IS CONTINUOUS AT EVERY POINT

ON THE INTERVAL

IF x* LIES IN THE INTERVAL

a < x* < b

THEN f IS CONTINUOUS IFF FOR EVERY ? > 0,

THERE IS A ? > 0, SUCH THAT |f(x*) - f(x)| < ?

WHENEVER |x* - x| < ?

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