# 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
 Author: jojobean0203 ID: 203190 Card Set: pre req Updated: 2013-05-27 23:29:07 Tags: pre req Folders: Description: pre req Show Answers: