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Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.

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Constructing real numbers using Bolzano-Weierstrass Theorem? [closed]

$\mathbb{R}$ is generally constructed as equivalence classes of Cauchy sequences. As Cauchy Completeness and Archimedean Property together are equivalent to the Bolzano-Weierstrass Theorem, there shou …