Remarks (exercises)1- R* is not field (why ?).2- Any nonempty set in R* has a sup and inf in R* (why ?).3- If Ø + ACR, is not bounded above in R, then sup A == co in R* (why ?).3- N, Z, Q are not bounded in R, while it is bounded in R*, and= oo in R* (why ?).sup N = sup Z = sup Q :

Noations:ℝ* denote the extended real number system s.t ℝ*=ℝ∪{-∞,+∞}.Complete set :A set S is said to…

Answered: Remarks (exercises) 1- R* is not field…

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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Remarks (exercises) 1- R* is not field (why ?). 2- Any nonempty set in R* has a sup and inf in R* (why ?). 3- If Ø + ACR, is not bounded above in R, then sup A = = co in R* (why ?). 3- N, Z, Q are not bounded in R, while it is bounded in R*, and = oo in R* (why ?). sup N = sup Z = sup Q :

Remarks (exercises) 1- R* is not field (why ?). 2- Any nonempty set in R* has a sup and inf in R* (why ?). 3- If Ø + ACR, is not bounded above in R, then sup A = = co in R* (why ?). 3- N, Z, Q are not bounded in R, while it is bounded in R, and = oo in R (why ?). sup N = sup Z = sup Q :