# Show that |R × R| = |R|. [Hint: Use the Schröder- ## Problem 35E Chapter 2.SE

Discrete Mathematics and Its Applications | 7th Edition

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Problem 35E

Show that |R × R| = |R|. [Hint: Use the Schröder- Bernstein theorem to show that |(0, 1) × (0, 1)| = (0, 1)|. To construct an injection from (0, 1) × (0, 1) to (0, 1), suppose that (x, y) ∈ (0, 1) × (0, 1). Map (x, y) to the number with decimal expansion formed by alternating between the digits in the decimal expansions of x and y, which do not end with an infinite string of 9s.]

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##### ISBN: 9780073383095

This full solution covers the following key subjects: decimal, show, hint, alternating, Der. This expansive textbook survival guide covers 101 chapters, and 4221 solutions. This textbook survival guide was created for the textbook: Discrete Mathematics and Its Applications, edition: 7th. Since the solution to 35E from 2.SE chapter was answered, more than 235 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 35E from chapter: 2.SE was answered by , our top Math solution expert on 06/21/17, 07:45AM. The answer to “Show that |R × R| = |R|. [Hint: Use the Schröder- Bernstein theorem to show that |(0, 1) × (0, 1)| = (0, 1)|. To construct an injection from (0, 1) × (0, 1) to (0, 1), suppose that (x, y) ? (0, 1) × (0, 1). Map (x, y) to the number with decimal expansion formed by alternating between the digits in the decimal expansions of x and y, which do not end with an infinite string of 9s.]” is broken down into a number of easy to follow steps, and 80 words. Discrete Mathematics and Its Applications was written by and is associated to the ISBN: 9780073383095.

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Show that |R × R| = |R|. [Hint: Use the Schröder-

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