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.9. Which is true for a nonempty subset S of R? O If S is nonempty and sup S exists, then S is bounde O If msx for all x ES, then m = sup S. O If m and n are suprema of S, then m = n. O If m = sup S, then m e S. O None of the above

.9. Which is true for a nonempty subset S of R? O If S is nonempty and sup S exists, then S is bounde O If msx for all x ES, then m = sup S. O If m and n are suprema of S, then m = n. O If m = sup S, then m e S. O None of the above

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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.9. Which is true for a nonempty subset S of R? * O If S is nonempty and sup S exists, then S is bounded. O If m sx for all x ES, then m sup S. If m and n are suprema of S, then m n. O If m = sup S, then me S. O None of the above 10. All are equivalent but which among the following versions was due to Archimedes as recalled in his works by a mathematician in 1880's? * The set N of natural numbers is unbounded above. O For each real number x, there exists a natural numbern such that n> x. O For each positive real x, and for each real number y, there is a natural numbern such that nx > y. O For each positive real x, there is a natural number n such that 0 < 1/n < x. O None of the above
Transcribed Image Text:.9. Which is true for a nonempty subset S of R? * O If S is nonempty and sup S exists, then S is bounded. O If m sx for all x ES, then m sup S. If m and n are suprema of S, then m n. O If m = sup S, then me S. O None of the above 10. All are equivalent but which among the following versions was due to Archimedes as recalled in his works by a mathematician in 1880's? * The set N of natural numbers is unbounded above. O For each real number x, there exists a natural numbern such that n> x. O For each positive real x, and for each real number y, there is a natural numbern such that nx > y. O For each positive real x, there is a natural number n such that 0 < 1/n < x. O None of the above
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