Triple

Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).

Phrase: A sequence (x_n) in a metric space (X,d) is Cauchy if for every ε > 0 there exists N such that for all m,n ≥ N, d(x_m,x_n) < ε. | Statement: [Cauchy sequence, hasDefinition, A sequence (x_n) in a metric space (X,d) is Cauchy if for every ε > 0 there exists N such that for all m,n ≥ N, d(x_m,x_n) < ε.]

Target entity: A sequence (x_n) in a metric space (X,d) is Cauchy if for every ε > 0 there exists N such that for all m,n ≥ N, d(x_m,x_n) < ε.
Context triple: [Cauchy sequence, hasDefinition, A sequence (x_n) in a metric space (X,d) is Cauchy if for every ε > 0 there exists N such that for all m,n ≥ N, d(x_m,x_n) < ε.]

• A. Cauchy sequence chosen
  A Cauchy sequence is a sequence whose terms become arbitrarily close to each other as the sequence progresses, providing a fundamental criterion for convergence in metric and normed spaces.
• B. Cauchy convergence criterion
  The Cauchy convergence criterion is a fundamental concept in mathematical analysis that characterizes convergence of sequences (and series) by requiring that their terms become arbitrarily close to each other beyond some index.
• C. epsilon–delta definition of limit
  The epsilon–delta definition of limit is the rigorous formalization of the intuitive notion of a function approaching a value, forming the foundation of modern analysis and calculus.
• D. Weierstrass M-test
  The Weierstrass M-test is a criterion in real and complex analysis that provides a sufficient condition for the uniform convergence of a series of functions by comparing it to a convergent series of bounding constants.
• E. Cauchy condensation test
  The Cauchy condensation test is a convergence criterion in mathematical analysis that determines whether an infinite series with positive, nonincreasing terms converges by comparing it to a related series formed by powers of two.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.