Using that result, prove by induction that for any positive integer ?, an infinite ?-dimensional array is countable.

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.5: Mathematical Induction
Problem 42E
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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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