pre req

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Author:
jojobean0203
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203190
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pre req
Updated:
2013-05-27 19:29:07
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pre req
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pre req
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  1. types of #
    • N    Natural numbers
    • W   Whole numbers
    • Z    Integers
    • Q    Rational numbers
    • I     Irrational numbers
    • R    Real numbers
  2. natural numbers
    • counting numbers
    • 1, 2, 3
    • subset of whole numbers, contained in the set of integers, which is inside the set of rational numbers
    • x + 2 = 5     {1, 2, 3, ....
  3. whole numbers


    • {0, 1, 2, 3, ...
    • natural numbers + 0
    • positive numbers
    • excludes: fractions, decimals
    • subset of integers
  4. integers


    • {0, + 1, + 2, + 3...
    • whole numbers & negative numbers
    • positive numbers + negative numbers + 0
  5. rational numbers
    • Q

    • integers + fractions + decimals
    • includes repeating/terminating decimals: 0.54444
    • real # that can be written as ratio of integers c non-zero denom
  6. irrational numbers
    • can't be expressed as ratio of 2 numbers
    • real numbers that aren't rational

    excludes: integers, fractions
  7. real numbers
    • rational + irrational numbers;
    • natural numbers + whole numbers
    • integers
    • fractions & decimals
  8. set
    • collection of distinct items without repeating
    • i.e.: natural #s are subset of integers
  9. proof
    means by which math is validated
  10. use summation notation to denote average
  11. prove that adding two even numbers = an even number
    • 2 variables for even #: x    y
    • x = 2q   q is an element of Z (integer)
    • y = 2p   p is an element of Z (integer)

    • x + y
    • 2q + 2p = 2 (p + q)
    • therefore x + y is even
  12. find formula for adding 1 to n
    sum = 1 + 2 + 3+ ...  + n
    • 1 S = 1 + 2 + 3 + ... + (n-2) + (n-1) + n
    • 2S = n +(n-1) + (n-2) + ....  3 + 2 + 1
    • 1 + n = n + 1
    • 2 + (n-1) = n + 1
    • 3 + (n-2) = n + 1
    • ....
    • (n-2) + 3 = n + 1
    • (n-1) + 2 = n + 1
    • n + 1 = n + 1

  13. identify domain, range, inputs, co-domain, & image
    • A = inputs
    • B = co-domain
    • A is subset of B
    • domain (g) = A
    • image: set/collection of all outputs
    • image (g) is contained in co-domain

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