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Abelian group addition and multiplication algebra angle assemblage asymptotic lines axis becomes infinite Calculus of Variations Cantor cardinal number catenary circle circle of convergence coefficients commutative law complex consider contains continuous function corresponding curve defined definition denote dense-in-itself derivative determined element equation example exists factor finite interval finite jumps finite number fixed following theorem formula Fourier's constants Fourier's development Fourier's series given Hence hyperbola inequality intersection involutory lemma limit Math Mathematical minimum multiply perfect numbers negative normal series obtained operators of order ordinal orthogonal osculating plane parastroid plane at infinity point pair positive integers prime Proof of theorem prove rational numbers real numbers result roots ruled surface series of type solution sphere subclass surface system which satisfies tangent theory tion transformed trigonometric series uniformly convergent unit circle unit-element values vanishes zero-element