**Analysis of Set S in Rational Numbers***Consider the set* \( S = \{ r \in \mathbb{Q} : r^2 < 2 \} \).*In the realm of rational numbers (\(\mathbb{Q}\)), is there a least upper bound for this set?*---This question explores the concept of least upper bounds (suprema) within the set of rational numbers. Specifically, it asks whether a least upper bound exists for the set of rational numbers whose squares are less than 2. The notation and symbols used in the set definition indicate that we are considering elements \( r \) within the rational numbers (\( \mathbb{Q} \)) such that when squared, they are less than 2.This leads to an interesting discussion about the supremum in the context of rational numbers versus real numbers.

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Answered: Consider the set S = {r E Q : r² < 2}.…

Math

Advanced Math

Consider the set S = {r E Q : r² < 2}. In the land of rationale numbers is there a least upper bound to this set?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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#1 Thanks.