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Symbols The Key to Notation

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7/9/2013 Symbols 2 2 Operations Subtraction ( – ) Division ( / ) Notation … addition of negatives … multiplication of reciprocals + Addition ( ), Multiplication ( )

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7/9/2013 Symbols 3 3 Intervals Open interval: ( a, b ) Closed interval: [ a, b ] Half-open/half-closed: [ a, b ), ( a, b ] Notation { x | a < x < b } = { x | a ≤ x ≤ b } =

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7/9/2013 Symbols 4 4 Relations Symbols: = ≠ ≤ ≥ Special Symbols ± ∆ Notation ∞ Binary Relations

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7/9/2013 Symbols 5 5 Irrational Numbers Not solutions of a x + b = 0 Algebraic numbers – roots of n th degree polynomials with rational coefficients Examples: x 2 – 2 = 0 x 3 – 5 = 0 Transcendental numbers Subsets of the Real Numbers { x | x R, x Q } x = 2 + – 3 5

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7/9/2013 Symbols 6 6 Irrational Numbers Not solutions of a x + b = 0 Transcendental numbers – Examples: = 3.1415 92653 58979 32384 62643 … e = 2.7182 81828 45904 52353 60287 … Subsets of the Real Numbers { x | x R, x Q } NOT roots of any polynomial with rational coefficients

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7/9/2013 Symbols 7 7 Calculations with Data Absolute value The unsigned “size” of a number Definition: a = a, for a ≥ 0 – a, for a < 0 For any real number a the absolute value of a, written, is a

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7/9/2013 Symbols 8 8 Calculations with Data Examples 1. 2. 3. 4. 7 = 7 = 3 0 = 0 Question: If a is any real number … … is – a positive or negative ? – 3 so a = ( 3) = 3 – – – Here a = 3 – – x 5 – – + =, for x ≥ 5, for x < 5

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7/9/2013 Symbols 9 9 Scientific Notation Standard notation 38100059018442 –60850017290000.00049487173 –0.2974615490024 Scientific notation 3.8100059018442 x 10 13 –6.085001729 x 10 13 4.9487173 x 10 – 4 –2.974615490024 x 10 – 1

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7/9/2013 Symbols 10 General form For real number r, scientific notation is r = c x 10 n where n is an integer and 1 ≤ Constant c usually a single-digit integer 10 Scientific Notation c < 10

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7/9/2013 Symbols 11 Think about it !

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