Definitions

ALGORITHM: An algorithm is a finite description of steps that transforms a valid input into an output.
ALGORITHMIC PROBLEM: An algorithmic problem is a description of valid inputs, required outputs, and the condition that connects every correct output with its input.
BIG O NOTATION: Big O notation gives an asymptotic upper bound: f(n) = O(g(n)) if, from some point onward, f(n) is no larger than a constant times g(n).
BIG OMEGA NOTATION: Big Omega notation gives an asymptotic lower bound: f(n) = Ω(g(n)) if, from some point onward, f(n) is at least a constant times g(n).
DISJOINT SETS Open article: Disjoint sets are sets that have no common elements.
EMPTY SET Open article: The empty set is a set that contains no elements.
LITTLE O NOTATION: little o notation gives a strict upper bound: f(n) = o(g(n)) if the ratio of f(n) to g(n) tends to zero.
LITTLE OMEGA NOTATION: little omega notation gives a strict lower bound: f(n) = ω(g(n)) if the ratio of f(n) to g(n) tends to infinity.
LOOP INVARIANT: A loop invariant is a statement that is true before the loop starts and remains true after every iteration.
PARTIAL CORRECTNESS: Partial correctness means: if the algorithm terminates on a valid input, then its result satisfies the postcondition of the problem.
PROPER SUBSET Open article: A proper subset is a subset that is not equal to the original set and therefore contains fewer elements.
RECURRENCE RELATION: A recurrence relation is a formula that expresses the cost of a problem through the cost of smaller problems of the same kind and the work done outside those subproblems.
SET Open article: A set in mathematics is a collection of unique elements, which may be numbers, symbols, or other objects.
SET DIFFERENCE Open article: The difference of sets A and B is the set of elements that belong to A but do not belong to B.
SET EQUALITY Open article: Two sets are equal if they contain exactly the same elements.
SET INTERSECTION Open article: The intersection of sets is the set that contains only the elements that belong to both sets.
SET UNION Open article: The union of sets is the set that contains all elements from both sets.
SPACE COMPLEXITY: Space complexity is a function that estimates the extra memory used by an algorithm as a function of input size.
SUBSET Open article: A subset is a set whose every element also belongs to another set.
TERMINATION: Termination means: the algorithm finishes on every valid input.
THETA NOTATION: Theta notation gives a tight asymptotic estimate up to constant factors: f(n) = Θ(g(n)) if both f(n) = O(g(n)) and f(n) = Ω(g(n)) hold.
TIME COMPLEXITY: Time complexity is a function that estimates the number of elementary operations performed by an algorithm as a function of input size.
TOTAL CORRECTNESS: Total correctness means partial correctness together with termination.