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Let {an} be a Cauchy sequence. The equivalence class of this sequence is a real number. Construct the Dedekind cut (AB) which presents this real number. Specifically, you need to come up with a way to produce the set AC Q (then B = Q\A) out of the sequence of (rational) numbers {an}.

Let {an} be a Cauchy sequence. The equivalence class of this sequence is a real number. Construct the Dedekind cut (AB) which presents this real number. Specifically, you need to come up with a way to produce the set AC Q (then B = Q\A) out of the sequence of (rational) numbers {an}.

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.2: Sequences, Series And Summation Notation
Problem 42E
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Let {an} be a Cauchy sequence. The equivalence class of this sequence is a real number. Construct the Dedekind cut (AB) which presents this real number. Specifically, you need to come up with a way to produce the set AC Q (then B = Q\A) out of the sequence of (rational) numbers {an}.
Transcribed Image Text:Let {an} be a Cauchy sequence. The equivalence class of this sequence is a real number. Construct the Dedekind cut (AB) which presents this real number. Specifically, you need to come up with a way to produce the set AC Q (then B = Q\A) out of the sequence of (rational) numbers {an}.
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