Show that there is no infinite set A such that | A|
SolutionStep 1In this problem, we have to show that there is no finite set A such that |A| < | Z+| = N0Let us assume that A be a infinite sets then it contains a countable infinite subject. So if A to Z+ be a one to one function then A and Z+ be a countable function.Here, Z+ be countable function then According to the theorem if X be a infinite sets then it contain an infinite countable sets. a1, a2, a3, ……….an Z+ where a1, a2, a3, ……….an be an element of set A.So, if the cardinality of Z+ is less than A then we can say that |A| < | Z+|.Hence, it is proved that there is no finite set A such that |A| < | Z+| = N0
Textbook: Discrete Mathematics and Its Applications
Author: Kenneth Rosen
The answer to “Show that there is no infinite set A such that | A|<|Z+| = N0.” is broken down into a number of easy to follow steps, and 14 words. This full solution covers the following key subjects: infinite, set, show, such. This expansive textbook survival guide covers 101 chapters, and 4221 solutions. This textbook survival guide was created for the textbook: Discrete Mathematics and Its Applications, edition: 7. Since the solution to 24E from 2.5 chapter was answered, more than 276 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 24E from chapter: 2.5 was answered by , our top Math solution expert on 06/21/17, 07:45AM. Discrete Mathematics and Its Applications was written by and is associated to the ISBN: 9780073383095.