Let K be greater than 0 and let f : Real numbers --> Real numbers satisfy the condition |f(x)-f(y)| less than or equal to K|x-y| for all x, y in Reals.

Show that f is continuous at every point in c in Reals.

Thank you.

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- Oct 20th 2009, 02:56 PMgixxer998Show a function is continuous at every point in Reals
Let K be greater than 0 and let f : Real numbers --> Real numbers satisfy the condition |f(x)-f(y)| less than or equal to K|x-y| for all x, y in Reals.

Show that f is continuous at every point in c in Reals.

Thank you. - Oct 20th 2009, 03:31 PMPlato
- Oct 20th 2009, 04:13 PMgixxer998
- Oct 20th 2009, 04:45 PMKrizalid
that's Lipschitz condition, and every Lipschitz function is uniformly continuous, hence continuous.

Plato is telling you to pick that $\displaystyle \delta$ to show the uniform continuity.