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Chapter 1 1.1 Properties of Real Numbers Real numbers – any # you can think of. From -∞ to +∞ Real Numbers Irrational Numbers Rational Numbers ``` Non Integer Rational Integers Negative Integers Whole Numbers Zero Natural Numbers Irrational Number – is any number that can be written as an infinite, nonrepeating decimal. 3 , 11 example = π, e, Not a perfect square. Decimal part does not repeat themselves. Decimal part does not terminate. Rational Number – is any number that can be written in the form a/b where a and b are integers and b ≠ 0. example = 3.14, 600, ¼, 3.13131313 Decimal part terminates. Decimal part repeats itself. Integers – Whole numbers from -∞ to +∞ with no fractional part. example = -123, -122, …. -3, -2, -1, 0, 1, 2, 3, …. 122, 123, etc. Non Integer Rational Numbers – all rational Numbers that are not integer. example = -1/4, 8.75, 2/3, -.45 Negative Integers – from -∞ to -1, with no fractional parts. example = -100, -99, …-3, -2, -1 Whole Numbers – Integer Numbers from 0 to +∞ with no fractional part. example = 0, 1, 2, 3, ….100, 101, …..+∞ Natural Numbers – Integer Numbers from 1 to +∞ with no fractional part. Inequality Symbols < > ≥ ≤ less than greater than greater than or equal to less than or equal to Field Properties of Real Numbers Addition A1 a + b is a real number Name of Property Closure Multiplication M1 a * b is a real number A2 a+b=b+a Commutative M2 a*b=b*a A3 (a + b) + c = a + (b + c) Associative M3 (a * b) * c = a * (b * c) A4 a+0=0+a=a Identity M4 a*1=1*a=a A5 a + ( -a ) = 0 Inverse M5 a * 1/a = 1 (a≠0) D Distributive Property a * ( b + c ) = a * b + a * c or ( b + c ) * a = b * a + c * a 1.2 Operations with Real Numbers Absolute Value 1. Distance between that number and zero. 2. A non negative number. 3. Non negative number always includes zero. 4. Use 2 vertical lines. x XX if x is positive or 0, X = X ; if x is negative, if x 0 if x 0 Order of operations Please Excuse My Dear Aunt Sally 1. ( ) 2. Exponents 3. Multiplication and Division 4. Addition and Subtraction X = -X