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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.

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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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.
Transcribed Image Text: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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