and are real numbers. If for all real numbers , then show that .
JNU SSS 2017 Question 49: Real analysis
Answer and worked solution
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Plain-text version
a and b are real numbers. If a < b + ε for all real numbers ε > 0, then show that a ≤ b.
Also written as: a and b are real numbers. If a < b + epsilon for all real numbers epsilon > 0, then show that a <= b.
Real analysis has come up 38 times in 5 exams since 2005.
What this question tests
This question is on Supremum, infimum and epsilon arguments, part of Real analysis in Mathematics.
Greatest lower and least upper bounds, and proofs that work with arbitrarily small tolerances.
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