## properties of real numbers notes pdf

The absolute value of a real number x, denoted by jxj, refers to the distance from that number to the origin of the number line, the point corresponding to 0. jxj= 8 >> < >>: x if x 0 x if x<0 Note. Use a calculator to approximate Ï} 6 to the nearest tenth: Ï} 6 ø . [a;b) is the set of all real numbers xwhich satisfy a x 0. which we calculate first) (a + b) + c = a + (b + c) 3. Example 1.1. Two fundamental partial order relations are the “less than or equal to (<=)” relation on a set of real numbers and the “subset (⊆⊆⊆⊆)” relation on a set of sets. These are some notes on introductory real analysis. a+b is real 2 + 3 = 5 is real. Outer measures As stated in the following deﬁnition, an outer measure is a monotone, countably Algebra II Accelerated Name _____ 1.1 Properties of Real Numbers – Notes Sheet Date _____ Digits – Natural (Counting) Numbers – Whole Numbers – Integers – Rational Numbers – Irrational Numbers – Example 1: Write each rational number as a fraction and list what sets of numbers each belong to: a) b) c) Create a Number Line showing all of the numbers from Example 1: Explain the associative property of addition. VII given any two real numbers a,b, either a = b or a < b or b < a. The chart below is nice because it shows the addition and multiplication properties side by side do you can see the similarities and differences. Keystone Review { Properties of Real Numbers Name: Date: 1. Basic Properties of Real Numbers Commutative Laws: a+ b= b+ a, ab= ba Associative Laws: (a+ b) + c= a+ (b+ c), (ab)c= a(bc) Distributive Law: a(b c) = ab ac Cancellation Law: If c6= 0 then ac bc = a b An important consequence of the Cancellation Law is that the only way a product of two numbers can equal 0 is if at least one of the factors is 0. 24 23 22 21 210 3 4 Example 1 Graph real numbers on a number line a2_mnlaect353043_c01l01-07.indd 1-1 9/16/09 7:16:39 PM The following notation is used (a;b) is the set of all real numbers xwhich satisfy a