10:18 #EMU To 37%■ < A to show that the set of all open intervals with endpoints in Q union {+infty, -infty} is countable, define a function f from that collection into the Cartesian product of Q union {+infty,- infty} with itself by mapping the interval (a,b) to the ordered pair (a,b). That function is one-to-one, so the image has the same cardinality as the original collection. Since the image is a subset of that Cartesian product, which is countable, the image is countable. ||| D < Prove that the collection of all intervals in R with endpoints in Qu{to} is countable.

10:18 #EMU To 37%■ < A to show that the set of all open intervals with endpoints in Q union {+infty, -infty} is countable, define a function f from that collection into the Cartesian product of Q union {+infty,- infty} with itself by mapping the interval (a,b) to the ordered pair (a,b). That function is one-to-one, so the image has the same cardinality as the original collection. Since the image is a subset of that Cartesian product, which is countable, the image is countable. ||| D < Prove that the collection of all intervals in R with endpoints in Qu{to} is countable.

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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