UP TGT Mathematics Real Analysis Test Series - Part 2
In the metric space Q (rational numbers), a Cauchy sequence of rational numbers:
Type: MCQ • Marks: 1
In the metric space Q (rational numbers), a Cauchy sequence of rational numbers:
Options
A. Never converges
B. May converge to an irrational number outside Q
C. Is always unbounded
D. Always converges to a rational number
Explanation
Correct Answer: Option 2 (May converge to an irrational number outside Q). Cauchy General Principle: In R, a sequence converges if and only if it is a Cauchy sequence (|a_n - a_m| < epsilon for n, m >= N). Every Cauchy sequence in R is bounded and convergent.
Want to attempt the full test series with a timer and instant score? Purchase the package to unlock the complete test.
Purchase Now
UP TGTMathematics
Practice more
This page is indexed for search so students can find questions directly from Google.
