Question: Define, recursively, the set S: 1 (0, 0) S 2 if (a, b) S, then (a, b + 1) S if (a, b) S, then

Define, recursively, the set S:

1 (0, 0) S

2 if (a, b) S, then (a, b + 1) S

if (a, b) S, then (a + 1, b + 1) S

if (a, b) S, then (a + 2, b + 1) S

Prove, using structural induction, that for (a, b) S, a 2b.

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