Analysis Give an example (with brief explanation) of each of the following:(a) A Dedekind cut corresponding to an irrational number.(b) A complex number that has norm 2, and that is not a real number.

Answered: Give an example (with brief…

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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Question

Analysis

Give an example (with brief explanation) of each of the following:
(a) A Dedekind cut corresponding to an irrational number.
(b) A complex number that has norm 2, and that is not a real number.

Expert Solution

Step 1

What is Dedekind Cut:

Dedekind cuts are a technique used in mathematics to create real numbers from rational numbers. The rational numbers are divided into two sets, A and B, and the Dedekind cut occurs when A lacks the biggest element and all of A's elements are less than all of B's elements. The smallest element among the rationals in set B might or might not exist. The cut corresponds to the rational in B that has the least element among the rationals. If not, that cut specifies a singular irrational number that, roughly speaking, bridges the distance between A and B.

To Give:

We given an example of the following statements: