All are equivalent but which among the following versions was due to Archimedes as recalled in his works by a mathematician in 1880's

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter2: Working With Real Numbers
Section2.1: Basic Assumptions
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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?
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.
For each real number x, there exists a natural
number n such that n > x.
For each positive real x, and for each real
number y, there is a natural number n such
that nx > y.
For each positive real x, there is a natural
number n such that 0 < 1/n < x.
None of the above
Transcribed Image Text: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. For each real number x, there exists a natural number n such that n > x. For each positive real x, and for each real number y, there is a natural number n such that nx > y. For each positive real x, there is a natural number n such that 0 < 1/n < x. None of the above
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