A convergent sequence in a normed space eventually gets arbitrarily close to its limit, which means that its terms eventually get arbitrarily close to each other, satisfying the definition of a Cauchy sequence. However, the converse is not necessarily true in a general normed space. There can exist Cauchy sequences that do not converge. A Cauchy sequence in a complete normed space (also known as a Banach space) is guaranteed to converge.
Which of the following is a true statement in a normed space?
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This question is part of 📏 Arithmetic Aptitude within the broader 🧠 Aptitude Mastery subject and appears in the SPSC – Sindh Public Service Commission preparation collection. Reviewing the answer together with nearby questions helps reinforce the underlying concept and identify how it may appear in competitive exams.