Revision: Ito calculus
Stochastic process: \(X(t), t\in[0,\infty)\)
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Integer Reciprocal and Geometric Series
Note that
\(\frac{1}{3} = \frac{1}{4} + \frac{1}{16} + \frac{1}{64} + \frac{1}{256} + \cdots\)
In fact, we have
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Opposite of a Bloom Filter
Bloom filter gives a \(O(1)\)-efficient way to test for set memberships, but with false positives and no false negatives, i.e. it will tell you \(x\in S\) while actually it is not, but not vice versa.
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e and π
Comparing \(e^{\pi}\) and \(\pi^e\).
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Volume of n-ball
If we denote the Cartesian coordinate of a \(n\)-dimensional Euclidean space by a
\(n\)-vector \(\mathbf{x}\), then a \(n\)-ball centered at the origin with radius \(r\)
is the set of points that satisfy
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