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Let \(f_{0}(x) = e^{x}\), and for all \(n = 1,2,3,4,...\), let \(f_{n}(x)=e^{f_{n-1}(x)}\). If

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Let \(S_{n} = \{x \in \mathbb{N} \ : \ x \leq n \}\) be the set of the first \(n\) natural numbers.

Let \(p: \mathcal{P}(\mathbb{N}) \rightarrow \mathbb{N}\) be a ...

\[f(x) = \begin{cases} 0 + \beta \ : \ \lfloor x \rfloor \equiv 0 \mod 3 \\ 1 + \beta \ : \ \lfloor x \rfloor \equiv 1 \mod 3 \\ 2 + \beta \ : \ \lfloor x \rfloor \equiv 2 \mod 3 \\ \end{cases}\]

CALVIN National Laboratories has begun exploring the effects of refraction on small beams of light on a newly discovered planet. An infinitely thin laser is fired from at rest from ...

Two rigid hemispheres \(A\) and \(B\) with uniform volume density \(\rho\) have radii \(a\) and \(b,\) respectively. Hemisphere \(B\) has its flat face glued to a plane. Hemisphere \(A\) is ...

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