Salem's theorem: every Pisot number is a two-sided limit of Salem numbers
Kernel-checked Salem's theorem — every Pisot number is a limit point of Salem numbers from both sides (R. Salem, Algebraic Numbers and Fourier Analysis, D. C. Heath, 1963, Ch. III, Theorem IV, p. 30; origin R. Salem, Duke Math. J. 12 (1945)) — with both of Salem's constructions, each stated as a construction. Three compared statements carry the surface. (1) salem_theorem — the theorem for Pisot numbers: a real algebraic integer alpha > 1 every other complex root of whose minimal polynomial has modulus 0, a Salem number in (alpha - eps, alpha) and one in (alpha, alpha + eps). (2)…
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