Using that result, prove by induction that for any positive integer ?, an infinite ?-dimensional array is countable.
Using that result, prove by induction that for any positive integer ?, an infinite ?-dimensional array 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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While the Small Monster collector, researcher, and ecclesiastical historian was busy with marmosets, we showed in class that we can assign an integer order to the members of an infinite two-dimensional array; and thus, that infinite two-dimensional arrays are countable, and can be re-ordered as infinite one-dimensional arrays. Using that result, prove by induction that for any positive integer ?, an infinite ?-dimensional array is countable.
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