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# Math Defs

## Terms

undefined, object
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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)
A+0=A=0+A
Multiplicative Identity
A*1=A=1*A
Right Identity for Division
A/1=A
Right Identity for Subtraction
A-0=A
Identity
Aâ™€I=A=Iâ™€A
A+-A=0=-A+A
Multiplicative Inverse
A*1/A=1=1/A*A
Inverse
Aâ™€A-1=I=A-1 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
1-1 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
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
A--B= 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 half-planes 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

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