Lecture 10 Notes

# The part above the line is called the hypothesis or

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: set S to be the smallest set contained in N and satisfying the following two properties: S, and S, then n ¢ 2. whenever n 3 ¢ ¢ 1. 0 S. Deﬁnition 3 (Example of deﬁnition by rules of inference) S 3) ¢ (n S ¢ n ¢ 0 S Each entry is called a rule of inference, or just a rule; the horizontal line is read as an “if-then”. The part above the line is called the hypothesis or the antecedent; the part below the line is called the conclusion or the consequent. When there are two or more hypotheses listed, they are connected by an implicit “and.” A rule with no hypotheses is called an axiom. The rules are interpreted as saying that an integer n is in S if and only if the statement “n S” can be derived from the axioms by using the rules of inference ﬁnitely many times. ¢ These three deﬁnitions are entirely equivalent. We’ll move back and forth between them freely. 6 Deﬁnition 4 (list of integers, top-down) A Scheme list is a list of integers if and only if either 1. it is the empty lis...
View Full Document

## This document was uploaded on 03/17/2014 for the course CSG 111 at Northeastern.

Ask a homework question - tutors are online