Ch. 1: Introduction to Writing Proofs in Mathematics

statement (proposition)

a sentence that is either true or false but not true and false

conditional statement

a statement that can be written in the form "If P then Q" where P and Q are sentences (P is the hypothesis and Q is the conclusion)

even integer

an integer a where there exists an integer n so that a = 2n

odd integer

an integer a where there exists an integer n so that a = 2n + 1

natural numbers, N

positive whole numbers

integers, Z

closed under addition, multiplication, and subtraction, positive and negative

rational numbers, Q

real numbers that can be written as a quotient of two integers

real numbers, R

all real numbers; rational and irrational numbers