# Shared Flashcard Set

## Details

Discrete Math Final Definations
mcann
82
Mathematics
12/09/2010

## Additional Mathematics Flashcards

Term
Definition
Term
 Argument
Definition
 connected series of statements to establish a definite proposition
Term
 Bound Variable
Definition
 a variable that is quantified
Term
 Cartesian Product
Definition
 x two sets A and B is the set of all ordered pairs of (a,b) such that a member B b member A
Term
 Compound proposition
Definition
 Combination of multiple propositions.
Term
 Congruent modulo
Definition
 a%m= b%m or m|(a-b)
Term
 Contingency
Definition
 Proposition that is neither a tautology or a contradiction
Term
Definition
 Proposition that always evaluates to false
Term
 Contraposition
Definition
 p->q not q -> not p
Term
 Converse
Definition
 p->q q->p
Term
 Corollary
Definition
 Theorem who's truth follows directly from an accepted theorem
Term
 Deductive Argument
Definition
 Moves from accepted general principals to specific situation.
Term
 Discrete Mathematics
Definition
 encompasses the representation and study of collections of distinct objects
Term
 Disjoint set
Definition
 Intersection is the empty set
Term
 Domain of Discourse
Definition
 A collection of values from which a variable's value is drawn
Term
 Fallacy
Definition
 Argument constructed with improper inference.
Term
 GCD
Definition
 Largest integer such that i|x and i|y
Term
 Horn Clause
Definition
 Disjunction of predicates in which at most one of the predicates is not negated
Term
 Identity Matrix
Definition
 In is a nxn with ones down main diagonal
Term
 Inductive Argument
Definition
 Moves from specific observations to a general conclusion.
Term
 Inverse
Definition
 p -> q is not p -> not q
Term
 LCM
Definition
 smallest integer such that x|s and y|s
Term
 Lemma
Definition
 simple theorem whose truth is used to construct more complex theorems
Term
 Logically Equivalent
Definition
 Both propositions evaluate to the same result when presented with the same input
Term
 Mathematical Logic
Definition
 The use of formal languages and grammars to represent the syntax and semantics of computation.
Term
 Multiplication Principle
Definition
 S steps with n1 ways first n2 second etc. then n1*n2...ns ways to complete
Term
 Ordered pair
Definition
 Set of two items (a,b) (a,b) not equal (b,a) unless a=b
Term
 Partition of a set
Definition
 Separates its members into disjoint sets
Term
 Philosophical Logic
Definition
 The classical notion of 'logic' The study of thought and reasoning.
Term
 Pigeonhole principle
Definition
 n items in k boxes then one box has ceiling (n/k) items
Term
 Power set
Definition
 Set of all of A's subset including empty set.
Term
 Predicate
Definition
 A statement that includes one or more variables and will evaluate to either true or false when the variables are assigned values
Term
 Proof
Definition
 sound argument that establishes the truth of a theorem
Term
 Proposition / statement
Definition
 is a claim that is either true or false with respect to an associated context
Term
 Sequence
Definition
 Ordered range of a function from a set of integers to a set S.
Term
 Set
Definition
 Unordered collection of unique objects
Term
 Simple proposition
Definition
 A proposition that contains no logical operators.
Term
 Sound argument
Definition
 Valid argument that has true premises
Term
 Specious Reasoning
Definition
 Unsupported or improperly constructed argument
Term
 Subset
Definition
 A is a ███▐█ B if every member of A can be found in B
Term
 Symmetric matrix
Definition
 A = A^T
Term
 Tautology
Definition
 Proposition that always evaluates to true
Term
 Transposition of matrix
Definition
 Denoted A^T mxn = nxm rows and columns exchanged.
Term
 Unbound variable
Definition
 unquantified variable
Term
 Valid Argument
Definition
 Conclusion must follow from the hypothesis
Term
 Well Formed Formula
Definition
 A correctly structured expression of a language.
Term
 Y
Definition
 Codomain of f
Term
 algorithm
Definition
 set of instructions for performing a task
Term
 arithmetic sequence
Definition
 constant called common difference
Term
 basis
Definition
 trivial case handling
Term
 bijective
Definition
 injective and surjective
Term
 composite
Definition
 p>=2 and p is not prime
Term
 composition
Definition
 f o g h = f(g(x))
Term
 conjecture
Definition
 statement with unknown truth value
Term
 countable
Definition
 finite or countable infinite
Term
 countable infinite
Definition
 bijective mapping is to either of the sets Z* or Z+
Term
 domain of f
Definition
 X
Term
 equivalence relation
Definition
 reflexive symmetric and transitive
Term
 factor
Definition
 i and j positive integers. i %j = 0
Term
 finite set
Definition
 bijective mapping between it and set of cardinality n
Term
 function
Definition
 f: X -> Y is a relation from X to Y.
Term
 geometric sequence
Definition
 gn+1/gn common ratio
Term
 image
Definition
 f(n) = p p is image n is preimage
Term
 increasing sequence (non decreasing)
Definition
 in <= in+1
Term
 inductive
Definition
 complex problems are handled in terms of simplier versions
Term
 injective
Definition
 f(x) = y for at most one member of X
Term
 irreflexive partial order
Definition
 reflexive, antisymmetric and transitive
Term
 mapping
Definition
 f maps X to Y
Term
 matrix
Definition
 n-Dimensional collection of values
Term
 partial order
Definition
 reflexive, antisymmetric and transitive
Term
 permutation
Definition
 ordering of n distinct elements
Term
 prime
Definition
 only factors are 1 and then number also number > 2
Term
 proper subset
Definition
 a is ███ B A is a subset of B and A not equal B
Term
 r-permutation
Definition
 ordering of r-elemtn subset of n distinct elements
Term
 range of f
Definition
 set of all images of elements of X
Term
 recursive definition
Definition
 basis, inductive and sometimes external clause
Term
 strictly decreasing
Definition
 in> in+1
Term
 strictly increasing sequence
Definition
 in < in+1
Term
 string
Definition
 continuous finite sequence of zero or more elements of x are found within y in the same relative order.
Term
 surjective
Definition
 f's range is Y (range=codomain)
Term
 theorem
Definition
 Conjecture that is shown to be true
Term
 total order
Definition
 every pair of elements a,b are comparable
Supporting users have an ad free experience!