I was pretty happy that I held off purchasing a Jawbone UP wristband because users have reported massive failures. Since then, Jawbone has had to offer full refunds to anyone who made a claim. The Nike FuelBand reminds me of the UP, but unlike the UP it might actually work. Plus, it looks much cooler.
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Some great notes from Dr. Terence Tao’s lecture on compacity and metric spaces.
Metric spaces are sets with a measure of distance between each of its elements. Compact spaces are spaces in which each sequence (xn) admits a converging sub-sequence. This is called the Bolzano-Weierstrass property and such compact spaces are called sequencially compact. There is a more general way of defining a compact space, by saying that each of its open covers has a finite subcover.