/sci/ - Science & Math

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Stirling's Approximation: For positive integers, [math]n[/math], the value of the factorial function, [math]n![/math] is given asymptotically by [eqn]n!\approx \sqrt{2\pi n} n^n e^{-n}[/eqn]

Neumann's Separation Lemma: Let [math]G[/math] be a permutation group acting on an infinite set, [math]\Omega[/math] with no finite orbits. Then for any finite subsets, [math]\Gamma[/math] and [math]\Delta[/math] of [math]\Omega[/math] ,there exists a permutation [math]g\in G[/math] for which [math]\Gamma^{g}\cap \Delta = \emptyset [/math]