# Math 13 Ch2

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 Author: Mattyj1388 ID: 158264 Filename: Math 13 Ch2 Updated: 2012-10-23 12:48:31 Tags: Libral Arts math013 COD Folders: Description: General information Show Answers:

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1. Set
• A "Set" is a collection of objects. We use the symbols {} to indicate that the collection is a set.
• Example:
• N = {1, 2, 3, 4, 5, . . . .}
2. Element
• An element is a member of a set. We use the symbol ϵ (is an element of) to indicate when an element belongs to a set.
• Example:
• 3 ϵ {1, 2, 3, 4, 5, . . . }
3. What does each symbol look like?
Set =
Element =
Natural#'s =
Whole #'s =
Intagers =
Rational #'s =
• Set = {}
• Element = ϵ
• Natural#'s = N
• Whole #'s = W
• Intagers = I
• Rational #'s = Q
4. N =
• N = Natural #'s or
• {1, 2, 3, 4, 5, 6, . . . }
5. W =
• W = Whole #'s or
• {0, 1, 2, 3, 4, 5, 6, . . . .}
6. I =
• I = Intagers or
• {. . .-3, -2, -1, 0, 1, 2, 3, . . .}
7. Q =
• Q = Rational #'s or repeating/ending decimal value, or any fraction with intagers. Infanetly many points between to points.
• Example:
• Q={a/b|a ϵ I and b ϵ I and b ≠ 0}
8. Well-defined set
• A set is well-defined if we are able to tell whether any particular object is an element of the set.
• Note: Q > I > W > N
9. Null Set
• The set that contains no elements is called the empty set or null set. This set is labeled by the or {} but not {}. {} means that an empty set is contained in an empty set. Every set has the empy set as a subset.
• Note: = {} = Empty set
10. Universal set
The universal set is the set of all elements under consideration in a given discussion. We often denote the universal set by the capital letter U.
11. Subset
The set A is a subset of the set B if every element of A is also an element of B.
12. Proper subset
The set A is a proper subset of the set B if A B but AB.
13. Sets containing subsets
• A set can be a set of subsets.
• Example:
• Since N Q
• and W Q
• then NWQ
14. Finite set
• The number of subsets of a finite set can be found by finding the cardinal number of the set. A set that has k elements has 2k subsets.
• Example:
• A={(HH),(HT), (TH),(TT)} the set is finite and n(A) = 4. therefore 24 = 16 subsets.
• Note: Pascals triangle to find subsets.
15. Cardinal #:
The Cardinal number is k in the finite set, or in other words, it is the total number of elements in the list.
16. Equivalent Sets
• Sets A and B are equivalent, or in One-to-One correspondence, if n(A) = n(B).
• Example:
• A={1, 2, 3, 4} ; B={a, b, c, d} then A and B are equivalent.

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