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95 Cards in this Set
- Front
- Back
N=Natural or counting numbers
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{1,2,3,4,...}
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W=Whole Numbers
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{0,1,2,3,...}
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I or z = integers
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{...,-3,-2,-1,0,1,2,3,...}
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Q=Rational Numbers
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All numbers that can be expressed as a ratio of I
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R=Real numbers
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All the numbers on the number line
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C=Complex Numbers
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a+b i | a,b=R i is the square root of -1
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Density
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A set is dense if between every pair of elements is another element
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Number
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An Idea concerning amount
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Numeral
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A symbol that represents a number
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Digit
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A symbol used to make a numeral
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Commutative Property of +
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A+B=B+A
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Commutative Property of *
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A*B=B*A
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Commutative Property
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A♀B=B♀A
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Associative property of +
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(A+B)+C=A+(B+C)
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Associative Property of *
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(A*B)*C=A*(B*C)
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Associative Property
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(A♀B)♀C=A♀(B♀C)
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Additive Identity
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A+0=A=0+A
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Multiplicative Identity
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A*1=A=1*A
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Right Identity for Division
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A/1=A
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Right Identity for Subtraction
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A-0=A
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Identity
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A♀I=A=I♀A
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Additive Inverse
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A+-A=0=-A+A
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Multiplicative Inverse
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A*1/A=1=1/A*A
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Inverse
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A♀A-1=I=A-1 ♀A
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Distributive Property
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A(B+C)= A*B=A*C
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Zero Product Theorem (ZPT)
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A*0=0=0*A
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Closure for subtraction of integers
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If every time you subtract an integer from another integer and come out with an integer, then subtraction is closed for integers
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Postulate(axiom)
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Statements that we accept as true with out proof
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Theorems
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Statements that we prove
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Cardinal Number
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Tells how many or the number of elements in a set
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Finite Set
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A set whose cardinal number can be represented by a whole number
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Infinite Set
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A set whose cardinal number can’t be represented by a whole number
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Equivelent Sets
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Sets with the same cardinal number
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1-1 correspondance
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Each member of set A is paired with a different member of set B with nothing left over in either set
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Successor
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The next one
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Predecesor
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the previous one
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Equal
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Sets with the same elements
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subset
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If every element of A is also an element of B, then A is a subset of B
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Empty Set
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The set with no elements
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Proper subset
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Any subset that doesn’t contain every element of the set
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Improper subset
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The set itself
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Super Set
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If every element of A is also an element of B then B is a super set of A
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power Set
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The power set of A is the set of all subsets of A
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Cardinal number of a power set
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2N When N is the cardinal number of the set
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Intersection
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The common members of two sets
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Union
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AUB is all the members of A together with all the members of B
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Universal Set
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The set of all elements being considered
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Set Complement
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All the members of the universe that aren’t in the set
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Patrician
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A patrician on set A is a set of pair wise disjoint subsets of A, such that their U is A
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Disjoint sets
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Sets whose intersection is {}
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conjunction
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compound sentence whose connecting word is and
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disjunction
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a compound sentence whose connecting word is or
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contradiction
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A logical statement that is false for all values of all variables
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Tautology
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A logical statement that is true for all values of all variables
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converse
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Given if A then B, The converse is If B then A
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contrapositive
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Given if B then A, The inverse is if –A then –B
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Equivelent statements
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Two statements whose Truth Values are the same for all values of all variables
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Subtraction
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A--B= A+-B
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Variable
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A symbol used to represent an element of a set
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Domain
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The set of all possible replacements for a variable
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Absolute Value
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|A| = {A if A is greater than or equal to 0
{-A if A is less than 0 |
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Factor
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If A*B=C then A and B are factors of C
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Multiple
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If A*B=C then C is a multiple of A and b
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prime
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A whole number >1 whose only factors are 1 & itself
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Composite
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A whole number >1 with more than 2 factors
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Relatively Prime
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Two numbers whose GCF is 1
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Fundamental Theorem of Arithmetic
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Any composite number that can be expressed as a unique product of primes
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GCF
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largest number that is a factor of each of two numbers
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LCM
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The smallest positive number that is a multiple of each of two numbers
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Perfect Numbers
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Numbers for which the sum of the proper factors is the number itself
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Abundant Numbers
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Numbers for which the sum of the proper factors is greater than the number itself
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Deficiant Numbers
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Numbers for which the sum of the proper factors is less than the number itself
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Amicable Numbers
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Two numbers for which the sum of the proper factors of each is the other.
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Line
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A straight set of points
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Plane
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A flat set of points
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Space
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The totality of all points
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Continuos
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no holes
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Infinite
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Contains an infinite number of points
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Demension
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A measurable quantity
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Seperation
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A geometric structure is separated by a boundary if we can’t get from one side to the other with out passing through the boundary
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Stationary
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Does not move
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Curve
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A set of points that can be traced with out picking up your pencil, crossing, or retracing
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Closed Curve
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A curve that begins and ends at the same point
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Simple Closed Curve
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a curve that is closed with no other point touched twice
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Vertex
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A point where 2 or more continuous sets of points intersect
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Dihedral Angle
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The union of 2 half-planes and their common line of intersection
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Probability
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The likely hood that an event will occur
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Sample Space
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the set of all possible outcomes for an experiment
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Combonation
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A set in which order doesn’t matter
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Permutation
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A set in which order does matter
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Factorial
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N! Is the product first N counting numbers
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Multiplication Principal
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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
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Independant Events
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Events that don’t effect the others
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Mutually Exclusive
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2 events that can’t occur at the same time.
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Conditional Events
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An event that occurs given the condition that a previous event has already occurred
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