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Constructive mathematics in the style of Bishop, including its semantics using realizabilty or topological methods.

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Axiom of choice and convergence

Hi fellows, I was wondering. Is the axiom of choice used to show that $\mathbb{R}$ is complete? If yes, is there a way to construct monotonic bounded sequences that do not converge? Thanks in advanc …
Jean-Luc Bouchot's user avatar