A SET Whose SUPREMUM is ∛10: sup{t ∈ ℝ | t ＞ 0 and t^3 ＜ 10} = ∛10

Описание: There is a clever Real Analysis strategy to prove the existence of ∛10 using the Completeness Axiom. By defining a non-empty bounded set whose supremum is the cube root of 10, we can link abstract set properties to a concrete number.

Rudin’s approach is to take E= {t ∈ ℝ | t ＞ 0 and t^3 ＜ 10}, which forms the open interval from 0 to ∛10, and ultimately prove that sup(E) = ∛10. This visualized in Mathematica reveals why ∛10 is the least upper bound of 𝐸, and therefore exists as a real number. This method showcases the power of the supremum property and why completeness is a cornerstone of real analysis.

📖 Visual Complex Analysis, by Tristan Needham: https://amzn.to/4d18FMP.

The SUPREMUM of this BOUNDED Set is the Cube Root of 10

#Supremum #RealAnalysis #CubeRootOf10 #BoundedSet #CompletenessAxiom #MathProofs #RealNumbers #MathematicsEducation #BabyRudin #IrrationalNumbers

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