Use the Cauchy Criterion to prove the Bolzano–Weierstrass Theorem, and find the point in the argument...

Use the Cauchy Criterion to prove the Bolzano–Weierstrass Theorem, and find the point in the argument where the Archimedean Property is implictly required. This establishes the final link in the equivalence of the five characterizations of completeness discussed at the end of Section 2.6.

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Colby Messinger answered 2 years ago

Use the Cauchy Criterion to prove the Bolzano–Weierstrass Theorem, and find the point in the argument...

Use the Cauchy Criterion to prove the Bolzano–Weierstrass Theorem, and find the point in the argument where the Archimedean Property is implictly required. This establishes the final link in the equivalence of the five characterizations of completeness discussed at the end of Section 2.6.

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What solutions did nineteenth-century analysts like Cauchy and Weierstrass find to the philosophical difficulties connected with infinitesimals?

prove every cauchy sequence converges

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Use the Cauchy Criterion to prove the Bolzano–Weierstrass Theorem, and find the point in the argument...

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Use the Cauchy Criterion to prove the Bolzano–Weierstrass Theorem, and find the point in the argument...

What solutions did nineteenth-century analysts like Cauchy and Weierstrass find to the philosophical difficulties connected with...

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