Math Defs
Terms
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 N=Natural or counting numbers
 {1,2,3,4,...}
 W=Whole Numbers
 {0,1,2,3,...}
 I or z = integers
 {...,3,2,1,0,1,2,3,...}
 Q=Rational Numbers
 All numbers that can be expressed as a ratio of I
 R=Real numbers
 All the numbers on the number line
 C=Complex Numbers
 a+b i  a,b=R i is the square root of 1
 Density
 A set is dense if between every pair of elements is another element
 Number
 An Idea concerning amount
 Numeral
 A symbol that represents a number
 Digit
 A symbol used to make a numeral
 Commutative Property of +
 A+B=B+A
 Commutative Property of *
 A*B=B*A
 Commutative Property
 Aâ™€B=Bâ™€A
 Associative property of +
 (A+B)+C=A+(B+C)
 Associative Property of *
 (A*B)*C=A*(B*C)
 Associative Property
 (Aâ™€B)â™€C=Aâ™€(Bâ™€C)
 Additive Identity
 A+0=A=0+A
 Multiplicative Identity
 A*1=A=1*A
 Right Identity for Division
 A/1=A
 Right Identity for Subtraction
 A0=A
 Identity
 Aâ™€I=A=Iâ™€A
 Additive Inverse
 A+A=0=A+A
 Multiplicative Inverse
 A*1/A=1=1/A*A
 Inverse
 Aâ™€A1=I=A1 â™€A
 Distributive Property
 A(B+C)= A*B=A*C
 Zero Product Theorem (ZPT)
 A*0=0=0*A
 Closure for subtraction of integers
 If every time you subtract an integer from another integer and come out with an integer, then subtraction is closed for integers
 Postulate(axiom)
 Statements that we accept as true with out proof
 Theorems
 Statements that we prove
 Cardinal Number
 Tells how many or the number of elements in a set
 Finite Set
 A set whose cardinal number can be represented by a whole number
 Infinite Set
 A set whose cardinal number canâ€™t be represented by a whole number
 Equivelent Sets
 Sets with the same cardinal number
 11 correspondance
 Each member of set A is paired with a different member of set B with nothing left over in either set
 Successor
 The next one
 Predecesor
 the previous one
 Equal
 Sets with the same elements
 subset
 If every element of A is also an element of B, then A is a subset of B
 Empty Set
 The set with no elements
 Proper subset
 Any subset that doesnâ€™t contain every element of the set
 Improper subset
 The set itself
 Super Set
 If every element of A is also an element of B then B is a super set of A
 power Set
 The power set of A is the set of all subsets of A
 Cardinal number of a power set
 2N When N is the cardinal number of the set
 Intersection
 The common members of two sets
 Union
 AUB is all the members of A together with all the members of B
 Universal Set
 The set of all elements being considered
 Set Complement
 All the members of the universe that arenâ€™t in the set
 Patrician
 A patrician on set A is a set of pair wise disjoint subsets of A, such that their U is A
 Disjoint sets
 Sets whose intersection is {}
 conjunction
 compound sentence whose connecting word is and
 disjunction
 a compound sentence whose connecting word is or
 contradiction
 A logical statement that is false for all values of all variables
 Tautology
 A logical statement that is true for all values of all variables
 converse
 Given if A then B, The converse is If B then A
 contrapositive
 Given if B then A, The inverse is if â€“A then â€“B
 Equivelent statements
 Two statements whose Truth Values are the same for all values of all variables
 Subtraction
 AB= A+B
 Variable
 A symbol used to represent an element of a set
 Domain
 The set of all possible replacements for a variable
 Absolute Value

A = {A if A is greater than or equal to 0
{A if A is less than 0  Factor
 If A*B=C then A and B are factors of C
 Multiple
 If A*B=C then C is a multiple of A and b
 prime
 A whole number >1 whose only factors are 1 & itself
 Composite
 A whole number >1 with more than 2 factors
 Relatively Prime
 Two numbers whose GCF is 1
 Fundamental Theorem of Arithmetic
 Any composite number that can be expressed as a unique product of primes
 GCF
 largest number that is a factor of each of two numbers
 LCM
 The smallest positive number that is a multiple of each of two numbers
 Perfect Numbers
 Numbers for which the sum of the proper factors is the number itself
 Abundant Numbers
 Numbers for which the sum of the proper factors is greater than the number itself
 Deficiant Numbers
 Numbers for which the sum of the proper factors is less than the number itself
 Amicable Numbers
 Two numbers for which the sum of the proper factors of each is the other.
 Line
 A straight set of points
 Plane
 A flat set of points
 Space
 The totality of all points
 Continuos
 no holes
 Infinite
 Contains an infinite number of points
 Demension
 A measurable quantity
 Seperation
 A geometric structure is separated by a boundary if we canâ€™t get from one side to the other with out passing through the boundary
 Stationary
 Does not move
 Curve
 A set of points that can be traced with out picking up your pencil, crossing, or retracing
 Closed Curve
 A curve that begins and ends at the same point
 Simple Closed Curve
 a curve that is closed with no other point touched twice
 Vertex
 A point where 2 or more continuous sets of points intersect
 Dihedral Angle
 The union of 2 halfplanes and their common line of intersection
 Probability
 The likely hood that an event will occur
 Sample Space
 the set of all possible outcomes for an experiment
 Combonation
 A set in which order doesnâ€™t matter
 Permutation
 A set in which order does matter
 Factorial
 N! Is the product first N counting numbers
 Multiplication Principal
 If Choice A can be made in M ways and choice B can be made in N ways then together they can be made in M*N ways
 Independant Events
 Events that donâ€™t effect the others
 Mutually Exclusive
 2 events that canâ€™t occur at the same time.
 Conditional Events
 An event that occurs given the condition that a previous event has already occurred