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Please mark all statements that are correct (there might be more than one correct answer). Ever open interval (a,b) ≤R, a

Please mark all statements that are correct (there might be more than one correct answer). Ever open interval (a,b) ≤R, a

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter8: Polynomials
Section8.2: Divisibility And Greatest Common Divisor
Problem 35E
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Please mark all statements that are correct (there might be more than one correct answer). Ever open interval (a,b) ≤R, a<b contains countably many rational numbers. The field of real numbers R is countable. n *. - (++-+-+-)*.· = n n Sequence x The set of all rational numbers Q is an ordered field that satisfies the Archimedean property but does not satisfy the monotone sequence property. Every monotone and bounded sequence {x} in R has limit in R. QUESTION 2 n EN converges in the Q. Mark all correct statements (there might be more than one correct answer). {x} be a real sequence such that x→ 5 then x - 5. n O Let x A sequence (x__》 of real numbers converges to x ER, if given ɛ > 0, we can find N E N, such that n n -x<& whenever n > N. If an ordered field satisfies Archimedean property then it also satisfy the monotone convergence property (MCP). If an ordered field F is complete then it satisfies the monotone sequence property. A sequence [x is bounded if for all n E N, there is M≥ 0, such that +|x₁|≤M. n
Transcribed Image Text:Please mark all statements that are correct (there might be more than one correct answer). Ever open interval (a,b) ≤R, a<b contains countably many rational numbers. The field of real numbers R is countable. n *. - (++-+-+-)*.· = n n Sequence x The set of all rational numbers Q is an ordered field that satisfies the Archimedean property but does not satisfy the monotone sequence property. Every monotone and bounded sequence {x} in R has limit in R. QUESTION 2 n EN converges in the Q. Mark all correct statements (there might be more than one correct answer). {x} be a real sequence such that x→ 5 then x - 5. n O Let x A sequence (x__》 of real numbers converges to x ER, if given ɛ > 0, we can find N E N, such that n n -x<& whenever n > N. If an ordered field satisfies Archimedean property then it also satisfy the monotone convergence property (MCP). If an ordered field F is complete then it satisfies the monotone sequence property. A sequence [x is bounded if for all n E N, there is M≥ 0, such that +|x₁|≤M. n
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