Definitions
General
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ba = b is a factor of a; there exists an integer c such that bc=a
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Prime = Let x be an integer. x is prime if x > 1 and the only positive factors of x are 1 and x
•
Composite = Let x be an integer. x is composite if there exists a b such that bx and 1<b<x
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Floor = Let x be a real number. The floor of x is the largest integer ≤x.
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Ceiling = Let x be a real number. The ceiling of x is the smallest integer ≥x.
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WLOG = without loss of generality
Sets
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List = An ordered collection
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Set = An unordered collection
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Cardinality = The size of a set, denoted A
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A=B = A and B are equal if every element of A is in B and vice versa.
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Subset = A is a subset of B if every element of A is also in B.
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Proper Subset = A is a proper subset of B if A ≠ B and A is a subset of B.
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Power Set = The power set of A is the set of all subsets of A, denoted by 2
A
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Set Difference = The set difference of AB is all elements that are in A but not in B.
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Symmetric Difference = The symmetric difference A∆B is the set of all elements that are in
A but not B or in B but not A.
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Universe = Let U denote the set of all objects under consideration. U is called the universe.
•
Complement = The complement of A, denoted Ā, is UA.
Relations
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 Fall '11
 BeryllCastello
 Natural number, r1, B. ·

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