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YCor
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Constructing Real Numbersreal numbers using Bolzano-Weierstrass Theorem?

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Ishan Deo
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Constructing Real Numbers using Bolzano-Weierstrass Theorem?

$\mathbb{R}$ is generally constructed as equivalence classes of Cauchy sequences. As Cauchy Completeness and Archimedean Property together are equivalent to the Bolzano-Weierstrass Theorem, there should be a method to construct $\mathbb{R}$ from $\mathbb{Q}$ using the Bolzano-Weierstrass Theorem.

So, is there such a method? If so, could someone point me towards some resources related to this?