4. Prove each of the following statements. (1) The set 2 of all integers is not an open subset of R. (ii) The set S of all prime numbers is a closed subset of R but not an open subset of R.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.1: Postulates For The Integers (optional)
Problem 1TFE: True or False Label each of the following statements as either true or false. The set Z of integers...
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necessarily a closed subset of R.
4. Prove each of the following statements.
(i) The set 2 of all integers is not an open subset of R.
(ii) The set S of all prime numbers is a closed subset of R but not an open subset of R.
Transcribed Image Text:necessarily a closed subset of R. 4. Prove each of the following statements. (i) The set 2 of all integers is not an open subset of R. (ii) The set S of all prime numbers is a closed subset of R but not an open subset of R.
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