The following are some notes taken during a lecture. Recursively Defined Functions Definition: A recursive or inductive definition of a function consists of two steps. BASIS STEP: Specify the value of the function at zero. RECURSIVE STEP: Give a rule for finding its value at an integer from its values at smaller integers. A function […]
Induction and Recursion
The following are some notes taken during a lecture. Mathematical Induction Suppose we have an infinite ladder: We can reach the first rung of the ladder. If we can reach a particular rung of the ladder, then we can reach the next rung. From (1), we can reach the first rung. Then by applying (2), […]
Logic and Proofs
The following are some notes taken during a lecture. Rules of Inference We have the two premises: “All men are mortal.” “Socrates is a man.” And the conclusion: “Socrates is mortal.” How do we get the conclusion from the premises? Rules of Inference: The Argument We can express the premises (above the line) and […]
Predicate Logic
The following are some notes taken during a lecture. Limitations of Propositional Logic If we have statements of the form: “All Purdue CS students are brilliant.” “Alice is a Purdue CS student.” Does it follow that “Alice is brilliant?” This is not easy to represent in propositional logic. We need a formalism (logic) that reasons […]
Propositional Logic
The following are some notes taken during a lecture. Propositions A proposition is a declarative sentence that is either true or false Examples: Neil Armstrong was a Purdue Alum. true Purdue Computer Science is in the Silicon Valley. false Purdue won the 2018 NCAA men’s basketball championship. false 1 + 0 = 1 true 0 […]