I live in a "rural" area. I live in a town of about 256 people and we are 16 miles from the nearest city of about 9,000 people. We have no problem at all getting electricity. There is a coal burning power plant and a hydroelectic dam that are close to me. Just because people live in the...
A function f:D\rightarrowR is called a Lipschitz function if there is some
nonnegative number C such that
absolute value(f(u)-f(v)) is less than or equal to C*absolute value(u-v) for all points u and v in D.
Prove that if f:D\rightarrowR is a Lipschitz function, then it is uniformly...
Suppose that S is a nonempty set of real numbers that is not Sequentially compact. Prove that either (i) there is an unbounded seqeunce in S or (ii) there is a sequence in S that converges to a point x0 that is not in S.
I am having trouble with this it not being sequentially compact is...