lentify the connect steps involved in proving that the set 2* x2 is countable. (Check all that apply.)
lentify the connect steps involved in proving that the set 2* x2 is countable. (Check all that apply.)
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
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Question
![Identify the corect steps involved in proving that the set 2x2 is countable. (Check all that apply.)
Check All That Apply
U
U
J
Define the sets A= [[In 2 where /belongs to Z. We can list the sets as A₁=[(1) Incz"), A₂ = {(2, 1)Incz¹), and so on.
For each define [n]) = (in), vec zª. Clearly, it is a one-to-one correspondence from the set of positive integers to the set A
From the definition of cardinality, each Ajis a countable set
From the definition of cardinality, each Ais an uncountable set.
Thus, we can think of 2" 2" as a union of countable number of countable sets A₂ A₂
Thus, we can think of 2 x 2 as a intersection of countable number of countable sets A₁, A2, -- A ---
We know that the union of countable number of countable sets is countable. Thus, 2*2* is countable](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F42a6310a-0eca-401e-bdf6-3b94c4cdd3e6%2Fffa5d6d3-6801-41ce-bac2-1884a1e04e01%2Fuple29_processed.png&w=3840&q=75)
Transcribed Image Text:Identify the corect steps involved in proving that the set 2x2 is countable. (Check all that apply.)
Check All That Apply
U
U
J
Define the sets A= [[In 2 where /belongs to Z. We can list the sets as A₁=[(1) Incz"), A₂ = {(2, 1)Incz¹), and so on.
For each define [n]) = (in), vec zª. Clearly, it is a one-to-one correspondence from the set of positive integers to the set A
From the definition of cardinality, each Ajis a countable set
From the definition of cardinality, each Ais an uncountable set.
Thus, we can think of 2" 2" as a union of countable number of countable sets A₂ A₂
Thus, we can think of 2 x 2 as a intersection of countable number of countable sets A₁, A2, -- A ---
We know that the union of countable number of countable sets is countable. Thus, 2*2* is countable
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