Show that any open interval (a, b) of the real numbers has the same cardinality as (0, 1). (note that b > a) Hint: Two sets A and B have the same cardinality if there exists a bijection from A to B, that is, it is possible to define a function from A → B, which is both one-to-one and onto
Show that any open interval (a, b) of the real numbers has the same cardinality as (0, 1). (note that b > a) Hint: Two sets A and B have the same cardinality if there exists a bijection from A to B, that is, it is possible to define a function from A → B, which is both one-to-one and onto
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
ChapterP: Prerequisites
SectionP.2: Real Numbers
Problem 3E: Express the set of real numbers between but not including 2 and 7 as follows. (a) In set-builder...
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Show that any open interval (a, b) of the real numbers has the same cardinality as (0, 1). (note that b > a)
Hint: Two sets A and B have the same cardinality if there exists a bijection
from A to B, that is, it is possible to define a function from A → B, which is both one-to-one and onto.
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