Ch 2.1 Objective: To recognize different sets of numbers and to identify a domain.

Definitions Natural Number 1, 2, 3, 4, …… (all the numbers you would include if you were to count from 1 to infinity) Whole Number 0, 1, 2, 3, 4, ….. (all of the natural numbers and 0) Integer -2, -1, 0, 1, 2, ……All of the whole numbers including positive numbers, negative numbers, and zero. Keep in mind that fractions are not integers. Rational Number -2/7, -1/2, 0/3, 4/5, 3/1………Any number which can be written as a fraction. Irrational Number Any number which can NOT be written as a fraction (a non-terminating & non-repeating decimal) Real Number -2, -1, -1/2, 0, ½, 1, 2, ………All of the Integers plus all of the fractions in between the whole numbers. Note: there are a few exceptions to this but you will learn about these numbers later. Positive Number ½, 1, 2, 100, ………….A number greater than 0. In other words, if x > 0, then x is a positive number. Negative Number -1/2, -1, -2, -100, ………A number less than zero. In other words, if x < 0, then x is a negative number.

Real Numbers Rationals Irrationals Any number which can be written as a fraction Non-terminating and non- repeating decimals which can’t be written as fractions. Examples:

Real Numbers Rationals Irrationals Any number which can be written as a fraction Non-terminating and non- repeating decimals which can’t be written as fractions. Examples:

Sets of Numbers Reals RationalsIrrationals - any number which can be written as a fraction., 7, Fractions/Decimals Integers, , … -3, -2, -1, 0, 1, 2, 3... Negative IntegersWholes … -3, -2, -10, 1, 2, 3... Zero 0 Naturals 1, 2, non-terminating and non-repeating decimals

Make a Venn Diagram that displays the following sets of numbers: Reals, Rationals, Irrationals, Integers, Wholes, and Naturals. Naturals 1, 2, 3... Wholes 0 Integers Rationals Irrationals Reals

Naturals 1, 2, 3... Wholes 0 Integers Rationals Irrationals Reals Imaginary Numbers

Identify all of the sets to which each number belongs. (Reals, Rationals, Irrationals, Integers, Wholes, Naturals) 1) -6 2) 3) 14 4) 6 Integer, Rational, Real Rational, Real Natural, Whole, Integer, Rational, Real Irrational, Real

Identify all of the sets to which each number belongs. (Reals, Rationals, Irrationals, Integers, Wholes, Naturals) 1) 0 2) ) 4) Whole, Integer, Rational, Real Rational, Real Irrational, Real Integer, Rational, Real

Graphing Real Numbers on a Number Line Graph the following numbers on a number line

Domain- the set of values which may be meaningfully substituted for a given variable. Which set of numbers would best describe the variable? 1) Let x = the number of people at a meeting. D : x Naturals “ is a member of ” 2) Let y = your weight D : y Positive Reals 3) Let t = the low temperature in Alaska yesterday D : t Reals 4) Let n = the low recorded temperature in Alaska. D : n Integers