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Mark all true statements (there might be more than one statement that is true). be a bounded sequence of real numbers, then Let {x} {x} has at least one cluster point. Let {x} be a sequence of real numbers. A number x ER is called a cluster point of {x} if and only if for every e > 0 and for every NE N there is k> № such that -x 0 and for every n EN there is k EN such that F₁-x/<0. Let L t {x} be a sequence of real numbers. A number x ER is called a cluster point of {x} if and only if for every >0 and for every N E N if k > N then ¹|x - x | < e. Let {x} be a sequence of real numbers. A number x ER is called a cluster point of {x} if for every e > 0, |x₁ - x|

Mark all true statements (there might be more than one statement that is true). be a bounded sequence of real numbers, then Let {x} {x} has at least one cluster point. Let {x} be a sequence of real numbers. A number x ER is called a cluster point of {x} if and only if for every e > 0 and for every NE N there is k> № such that -x 0 and for every n EN there is k EN such that F₁-x/<0. Let L t {x} be a sequence of real numbers. A number x ER is called a cluster point of {x} if and only if for every >0 and for every N E N if k > N then ¹|x - x | < e. Let {x} be a sequence of real numbers. A number x ER is called a cluster point of {x} if for every e > 0, |x₁ - x|

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 13E: 13. Consider the set of all nonempty subsets of . Determine whether the given relation on is...
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Mark all true statements (there might be more than one statement that is true). be a bounded sequence of real numbers, then [x has at least one cluster point. {x} Let {x Let {x} be a sequence of real numbers. A number x ER is called a cluster point of {x} if and only if for every &> 0 and for every NEN there is k > N such that Let [x be a sequence of real numbers. A number x ER is called a cluster point of [x if and only if for every & > 0 and for every n E N there is k € N such that |x₂-x | < e. Let Sx Let X be a sequence of real numbers. A number x E R is called a cluster point of [x n be a sequence of real numbers. A number x E R is called a cluster point of [x if and only if for every > > 0 and for every N E N if k > N then if for every ¹|x₁ - x| <e. E> >0, TK k -x<& holds for infinitely many k E N.
Transcribed Image Text:Mark all true statements (there might be more than one statement that is true). be a bounded sequence of real numbers, then [x has at least one cluster point. {x} Let {x Let {x} be a sequence of real numbers. A number x ER is called a cluster point of {x} if and only if for every &> 0 and for every NEN there is k > N such that Let [x be a sequence of real numbers. A number x ER is called a cluster point of [x if and only if for every & > 0 and for every n E N there is k € N such that |x₂-x | < e. Let Sx Let X be a sequence of real numbers. A number x E R is called a cluster point of [x n be a sequence of real numbers. A number x E R is called a cluster point of [x if and only if for every > > 0 and for every N E N if k > N then if for every ¹|x₁ - x| <e. E> >0, TK k -x<& holds for infinitely many k E N.
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