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

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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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