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### 26 Cards in this Set

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 Set A collection of unique elements. Union A and B = {x in X: x in A and x in B} Intersection A or B = {x in X: x in A or x in B} Complement A^(c) = {x in X: x NOT in A) Set Difference A\B = A and B^(c) = {x in A and x not in B} Symmetric Difference A tri B = (A or B)\(A and B) Onto (surjective) Let X,Y be sets and f:X to Y. We say that f maps X onto Y if for each y in Y, there exists a point x in X such that f(x) =y. in english, all the points in the domain must be hit. One to One (injective) Let X,Y be sets and f:X to Y. We say that f is one-to-one if each y in f(X) is mapped to by a unique element of X. Not all y in Y must be hit. Bijective both one to one and onto Domain the set the function is defined on Codomain all the values of the function. Range all the values in the Codomain which are mapped to. Well defined each point of x maps to exactly one point of Y. Cardinality Let A and B be sets. We say that A and B have the same cardinality, card(A) = card(B), if there is a bijection f: A to B. Cardinality of a finite set A set A is a finite set with cardinality n if card(A) = card(B) where B = {1,2,3,....,n}. In other words, the cardinality of set A is the number of elements in Cardinality of the empty set 0, no elements in the set Countable A set A is countable if card(A) = card(N) or A is finite Uncoutable otherwise Bounded above Let X be an ordered field and let A subset X be nonempty. We say A is bounded above if there is a point M in X such that a<=M for every a in A. Upper Bound M is the upper bound Bounded below A is bounded below if there is a point m in X such that m<=a for every a in A. Lower Bound Here m is the lower bound for A. Supremum (least upper bound) Let X be an ordered field and let A subset X be nonempty and bounded above. We say A has a supremum if there is a point in X, denoted sup(A), such that a. sup(A) is an upper bound for A; b. if b is another upper bound for A, then sup(A)<=b Complete We say that an ordered field X is complete if every set A subset X that is nonempty and bounded above has a least upper bound in X. Real number system We define the set R to be the complete ordered field containing Q as an ordered subfield. Absolute value function abs(x) = x, x>0 = 0, x = 0 = -x, x<0