UP TGT Mathematics Real Analysis Test Series - Part 2
If a set S of real numbers is bounded below, then its greatest lower bound (infimum) is:
Type: MCQ • Marks: 1
If a set S of real numbers is bounded below, then its greatest lower bound (infimum) is:
Options
A. Always an element of S
B. Non-existent in R
C. Always negative
D. Unique and real
Explanation
Correct Answer: Option 4 (Unique and real). The real numbers form a complete ordered field. Rational numbers fail completeness since bounded rational sets may lack rational supremum/infimum.
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