README.md

Happy Birds

Conditions

• The conditions of problem 6 hold
• We note that, in the definition of compatibility, A and B might be the same bird (compatible with itself), or the x and y inputs might be the same value
• A bird that is compatible with itself is called "happy": that is, for happy bird A, there exist birds x and y such that A(x) === y and A(y) === x

Problem

• Show that any bird that is fond of another must be happy

Solution

This one's simple. Recall that bird A is fond of bird x when A(x) === x, and that, in the definition of compatibility, x and y may be the same bird. A(x) === x automatically satisfies both A(x) === y and A(y) === x when x and y are the same. Thus, A will be compatible with itself, and happy.

Next =>