a. Which of the eight properties are satisfied by N? Give examples of the properties which are not satisfied by N. b. Which of the eight properties are satisfied by Z? Give examples of the properties not satisfied by Z.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.7: Distinguishable Permutations And Combinations
Problem 29E
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We will assume that the sets N and Z satisfy the following properties:
i. m, n e Z = m + n, m – n, m · n E Z
1
ii. n e Z then n E N n>1
iii. There is no n e Z that satisfies 0 < n < 1.
Notice that none of the special subsets N, No, Z, Q, and Qº satisfy Postulate One of the
field of real numbers R.
a. Which of the eight properties are satisfied by N? Give examples of the properties
which are not satisfied by N.
b. Which of the eight properties are satisfied by Z? Give examples of the properties
not satisfied by Z.
Transcribed Image Text:We will assume that the sets N and Z satisfy the following properties: i. m, n e Z = m + n, m – n, m · n E Z 1 ii. n e Z then n E N n>1 iii. There is no n e Z that satisfies 0 < n < 1. Notice that none of the special subsets N, No, Z, Q, and Qº satisfy Postulate One of the field of real numbers R. a. Which of the eight properties are satisfied by N? Give examples of the properties which are not satisfied by N. b. Which of the eight properties are satisfied by Z? Give examples of the properties not satisfied by Z.
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