gammarat

I'm not dead, yet.

Last quarter sucked at school. This quarter is better, so far. I'm still working as much but taking fewer classes. Hopefully, I'll be a little less harried.

Oh, well. Maybe, in the fiture, I'll pass along a cute new analysis or algebra fact from class each time. Well. Next time.

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Okay, I'll do it this time (but in linky-link form)

Consider a metric space (X, d) then let F be the set of all closed and bounded subsets of X. Now consider the Hausdorff metric on F.

Let f(x)=1/3x and g(x) = 1/3x + 2/3. Define G:F->F to be G(A) = f(A)Ug(A). Then G is a contraction. Which implies that for some set, A, in F G(A) = A. (It has a fixed point).

Taking the metric space [0,1] with the usual metric. The fixed point in this metric space is the Cantor Set.

Fun stuff.