_Real__ Numbers _System__ Rational Numbers Irrational Numbers 0.75 -1 Whole numbers Integers Natural Numbers Real Numbers The Set is a collection of _elements__ , listed within braces { }. A _subset_ is a set whose elements are all contained in another set. The set of positive integers, for example, is a subset of the set of integers_ . Natural numbers: The set of real numbers that begin with the number _ONE_ , The smallest set, also known as _counting numbers_ . Whole numbers builds from the set of natural numbers by adding the number _ZERO_ . Integers build from the set of _Whole numbers by adding negative “whole” numbers. Can be both positive and negative_, but there are no decimals_ ! Rational Numbers are RATIOs of two integers ( fractions ) The set builds from the set of _Integers by adding fractions. Also consist of terminating and repeating decimals. Irrational does not build up from the previous sets. It consists of not rational numbers with non-terminating , non-repeating decimals. First, SIMPLIFY, then ANALYZE parts of the number: If my number… has has has has has NO decimal part, NO decimal part, NO decimal part, DECIMAL PART DECIMAL PART NO negative sign NO negative sign, Ratio, It is NOT zero Is NEGATIVE Non-terminating, Terminating Decimal is ZERO (0) Repeating Decimal Non- Repeating Then start from… Natural Whole Integers Rational Irrational Then move toward REAL Numbers Sign (skip Irrational after Rational). Choose the starting point, and then move toward Real Sign Example Natural Whole Integer Choose only one: Real (counting (and ZERO) (and Rational Irrational (all of numbers: negatives) (AND repeating (OR non-terminating, them) 1, 2, 3, …) or terminating, non-repeating decimal part) decimal part) NO DECIMAL PART DECIMAL PART 0 √ √ √ √ 5 √ √ √ √ √ -9 √ √ √ = 5 √ √ √ √ √ √ √ √ √ 0.141414… √ √ 0.010110111… √ √ Name all sets of numbers to which each real number belongs. 1) 30 N, W, Z, Q, R 2) – 11 Z, Q, R 3) 5 Q, R 4) I, R 5) 0 W, Z, Q, R 6) Z, Q, R 7) N, W, Z, Q, R 8) I, R .