dense set Archives - Infinity is Really Big

June 7, 2021June 14, 2021

The Archimedean Property

The Completeness Axiom is a sufficient condition to prove the Archimedean Property, but is it necessary?

Real Analysis Study Help for Baby Rudin, Part 1.5

A Visualization of the Archimedean Property in the case where $x=8$ and $y=70$ . The smallest positive integer value of $n$ that makes $nx>y$ is $n=9$ .

x=8 — A Visualization of the Archimedean Property in the case where $x=8$ and $y=70$ . The smallest positive integer value of $n$ that makes $nx>y$ is $n=9$ .

Does the sequence $\left(\frac{1}{n}\right)_{n=1}^{\infty}$ approach zero as $n\rightarrow \infty$ ? Sure! After all, given any number

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