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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.)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.1: Real Numbers
Problem 35E
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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
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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