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The constructivitation of mathematics
Sequences and series of real numbers
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approximation arbitrary Assume Banach algebra Banach space Borel set bounded linear functional bounded subset called Cauchy sequence Chap Choose closed compact set compact subset complemented set complete complex numbers Consider consist continuous function converges Corollary countable defined Definition dense double norm equal equivalent everywhere exists follows function f given gives Hence hermitian operator Hilbert space hounded induced inequality input sequence integrable function integrable set inverse Let f Li(G locally compact space locally convex space martingale mathematics measurable functions measure space metric space modulus of continuity neighborhood nonnegative nonzero norm-preserving isomorphism normable linear functional normed linear space open set output sequence path positive constant positive integer positive measure Proof Let Proposition prove rational numbers real numbers satisfied seminorm simple function test function Theorem theory totally bounded uniformly continuous valid vector Write