The Way of Z

From Chapter 6

The state machine model did not specify the initial state. The only reasonable choice is the PATIENTS state.

From Chapter 10

beam = on ↔ door = closed means the beam is on when the door is closed and the beam is off when the door is open. This is a bad requirement because the beam will turn on the moment the door is closed.

beam = on ∧ door = closed means the beam is always on and the door is always closed. Obviously useless.

beam = on ∨ door = open means the beam is on or the door is open, or both. This is a bad requirement because it allows the beam to be on when the door is open.

beam = off ∨ door = closed means the beam is off or the door is closed, or both. This is a good requirement, and means exactly the same thing as beam = on ⇒ door = closed, according to the law p ⇒ q ⇔ ¬ p ∨ q.

x ∈ dom f ⇒ f x = y is true when x ∈ dom f is false, otherwise it has the same truth value as f x = y.

From Chapter 11

Represent each triangle as a tuple whose components are the lengths of its three sides. These tuples are called Pythagorean triples because their components are related by the Pythagorean theorem; (3, 4, 5) is a Pythagorean triple because 32 + 42 = 52.