1. Symbols The Key to Notation

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

3. 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 } =

4. 7/9/2013 Symbols 4 4 Relations Symbols: = ≠ ≤ ≥ Special Symbols       ± ∆   Notation  ∞ Binary Relations

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 7/9/2013 Symbols 11 Think about it !