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Let N= {1, 2, 3, 4, .} be the set of natural numbers and S= (1, 4, 9, 16, ...} be the set of squares of the natural numbers. Then N - S, since we have the one-to-one correspondence 1 + 1, 2 + 4, 3 + 9, 4 + 16, ... n+ n?. (This example is interesting, since it shows that an infinite set can be equivalent to a proper subset of itself.) Show that each of the following pairs of sets are equivalent by carefully describing a one-to-one correspondence between the sets. Complete parts (a) through (c) below. (a) The whole numbers and natural numbers, W = {0, 1, 2, 3, ..} and N= {1, 2, 3, 4, ...} Which of the following describes a one-to-one correspondence between the two sets? O A. For each element in W, there is an element in N that is double that element. O B. For each element in w. there is an element in N that is 1 areater than double that element.

Let N= {1, 2, 3, 4, .} be the set of natural numbers and S= (1, 4, 9, 16, ...} be the set of squares of the natural numbers. Then N - S, since we have the one-to-one correspondence 1 + 1, 2 + 4, 3 + 9, 4 + 16, ... n+ n?. (This example is interesting, since it shows that an infinite set can be equivalent to a proper subset of itself.) Show that each of the following pairs of sets are equivalent by carefully describing a one-to-one correspondence between the sets. Complete parts (a) through (c) below. (a) The whole numbers and natural numbers, W = {0, 1, 2, 3, ..} and N= {1, 2, 3, 4, ...} Which of the following describes a one-to-one correspondence between the two sets? O A. For each element in W, there is an element in N that is double that element. O B. For each element in w. there is an element in N that is 1 areater than double that element.

Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter2: Working With Real Numbers
Section2.1: Basic Assumptions
Problem 40WE
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Let N= {1, 2, 3, 4, .} be the set of natural numbers and S= (1, 4, 9, 16, ...} be the set of squares of the natural numbers. Then N - S, since we have the one-to-one correspondence 1 + 1, 2 + 4, 3 + 9, 4 + 16, ... n+ n?. (This example is interesting, since it shows that an infinite set can be equivalent to a proper subset of itself.) Show that each of the following pairs of sets are equivalent by carefully describing a one-to-one correspondence between the sets. Complete parts (a) through (c) below. (a) The whole numbers and natural numbers, W = {0, 1, 2, 3, ..} and N= {1, 2, 3, 4, ...} Which of the following describes a one-to-one correspondence between the two sets? O A. For each element in W, there is an element in N that is double that element. O B. For each element in w. there is an element in N that is 1 areater than double that element.
Transcribed Image Text:Let N= {1, 2, 3, 4, .} be the set of natural numbers and S= (1, 4, 9, 16, ...} be the set of squares of the natural numbers. Then N - S, since we have the one-to-one correspondence 1 + 1, 2 + 4, 3 + 9, 4 + 16, ... n+ n?. (This example is interesting, since it shows that an infinite set can be equivalent to a proper subset of itself.) Show that each of the following pairs of sets are equivalent by carefully describing a one-to-one correspondence between the sets. Complete parts (a) through (c) below. (a) The whole numbers and natural numbers, W = {0, 1, 2, 3, ..} and N= {1, 2, 3, 4, ...} Which of the following describes a one-to-one correspondence between the two sets? O A. For each element in W, there is an element in N that is double that element. O B. For each element in w. there is an element in N that is 1 areater than double that element.
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