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R.5. Define a relation < on the set of ordered pairs of real numbers (x, y) as follows: (X1:Vi)<(x,:Y2) if and only if (1) x

R.5. Define a relation < on the set of ordered pairs of real numbers (x, y) as follows: (X1:Vi)<(x,:Y2) if and only if (1) x

Advanced Engineering Mathematics
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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I need help with this discrete mathematics problem involving proving linear ordering

R.5. Define a relation < on the set of ordered pairs of real numbers (x, y) as follows: (X1, i)<(x,;Y2) if and only if (1) x, <x, or (2) x, = x, & y; S y;. Prove that < defines a linear ordering on the set of ordered pairs of real numbers. (This shows that the coordinate plane can be linearly ordered!)
Transcribed Image Text:R.5. Define a relation < on the set of ordered pairs of real numbers (x, y) as follows: (X1, i)<(x,;Y2) if and only if (1) x, <x, or (2) x, = x, & y; S y;. Prove that < defines a linear ordering on the set of ordered pairs of real numbers. (This shows that the coordinate plane can be linearly ordered!)
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