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The Constructivization of Mathematics
The Real Number System
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approximation arbitrary assume Banach space belongs bounded called Cauchy sequence Chapter Choose classical Clearly closed commutative compact integrable compact set complemented set complete Consider consisting constructive contained continuous function converges Corollary defined Definition dense differentiable function elements equal equivalence example exists extended fact finite follows full set function f given gives Hence holds induced inequality integrable function integrable set interval inverse Lemma limit linear functional located mathematics measure metric space modulus neighborhood nonnegative nonzero normable normed linear space Note obtain open set operator path positive integer positive measure positive number Proof Proposition prove real numbers relative respect result satisfies sequence sphere subset sufficiently Suppose test function theorem theory totally bounded uniformly continuous unique vector write