UNIFORM CONTINUITY

x1 AND x2 ARE IN AN INTERVAL

a < x < b

f(x) IS UNIFORMLY CONTINUOUS

ON THE INTERVAL

IFF FOR EVERY ? > 0,

THERE IS A ? > 0, SUCH THAT |f(x1) - f(x2)| < ?

WHENEVER |x1 - x2| < ?

THIS IS THE STRONGEST CONDITION SINCE IT

IS INDEPENDENT OF x.

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