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
- A♀B=B♀A
- Associative property of +
- (A+B)+C=A+(B+C)
- Associative Property of *
- (A*B)*C=A*(B*C)
- Associative Property
- (A♀B)♀C=A♀(B♀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
- A-0=A
- Identity
- A♀I=A=I♀A
- Additive Inverse
- A+-A=0=-A+A
- Multiplicative Inverse
- A*1/A=1=1/A*A
- Inverse
- A♀A-1=I=A-1 ♀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 can’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 doesn’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 aren’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 –A then –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 can’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 doesn’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 don’t effect the others
- Mutually Exclusive
- 2 events that can’t occur at the same time.
- Conditional Events
- An event that occurs given the condition that a previous event has already occurred