Math Problem Statement
Show that if (an)n∈N,(bn)n∈N are equivalent sequences, then (an)n∈N is Cauchy if and only if (bn)n∈N is Cauchy
Solution
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Math Problem Analysis
Mathematical Concepts
Real Analysis
Cauchy Sequences
Equivalent Sequences
Limits
Formulas
Definition of Cauchy Sequence: |a_n - a_m| < ε for all m, n > N
Definition of Equivalent Sequences: lim (n -> ∞) |a_n - b_n| = 0
Theorems
Cauchy Criterion
Triangle Inequality
Suitable Grade Level
College-level (Real Analysis)
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