Term

Definition
A ________ is an unordered collection of objects, where each object can appear (counts) only once. 


Term

Definition
A function
f : A → B is called ___________ if and only if for every element y ∈ B there is an element x ∈ A such that y = f (x). 


Term
Bijective (OnetoOne Correspondence) 

Definition
A function
f is called a _________________ if f is both onetoone and onto (both injective and surjective). 


Term

Definition
A function
f is ______________ if an only if f (a)= f (b) implies that a = b for all elements a and b in the domain of f . We
also say that
f is an injection. 


Term

Definition
A function defined on a subset of real numbers is called
________ if for any x < y we have that f (x) ≤f (y). 


Term

Definition
A function defined on a subset of real numbers is called
__________ if for any x < y we have that f(x) ≥ f(y). 


Term

Definition
A set
A is a _______ of a set B if for every x ∈ A we have also that
x
∈ B. 


Term

Definition
A _________ is a rule that associates to every element in a set
A (called domain), a single element in a set B (called range). 


Term

Definition
A _____________ is a sequence:
a, a · r , a · r², ..., a · r^{n}, ...where a is called the initial term and r is called the common ratio. 


Term

Definition
An _______ is a precise set of instructions (steps) for performing a computation or for solving a problem. 


Term

Definition
An ________________ is a sequence:
a, a + d, a + 2d, ..., a + nd, ...where a is called the initial term and d is called the common difference. 


Term

Definition
If
a, b are integers, b ≠ 0, we say that b divides a if there exists an integer c such that a = b⋅c.
We say that
b is a factor of a and that a is a multiple of b. 


Term

Definition
Let
U specify the universal set. The ________ of a set A, denoted Ā, is Ā = U − A. 


Term

Definition
Let
f , g be functions from the set of reals or integers to the set of reals. We say that f (x) is Ω(g(x)) if there are constants C and k such that:
f(x)
≥ C⋅g(x) for all x > k



Term

Definition
Let
f , g be functions from the set of reals or integers to the set of reals. We say that f (x) is Θ(g(x)) if f (x) is both O(g(x)) and Ω(g(x)). 


Term

Definition
Let
f , g be functions from the set of reals or integers to the set of reals. We say that f (x) is O(g(x)) if there are constants C and k such that:
f(x) ≤
C ⋅g(x) for all x > k 


Term
Division Algorithm Theorem 

Definition
Let a ∈ ℤ, d ∈ ℤ; d > 0. There exist unique integers q and r such that a = q⋅d + r , with 0 ≤r < d.
a = dividend
q = quotient
d= divisor
r= remainder 


Term
Representation of Integers Theorem 

Definition
Let b
> 1 an integer. Then any positive integer n can be uniquely expressed as:
n
= a_{k}⋅b^{k} + a_{k1}⋅b^{k1}+ ...+ a2⋅b^{2}+ a1⋅b + a0
where k ≥
0 and ak, a1, a0 are all nonnegative integers smaller than b. 


Term

Definition
The ______of sets
A and B, denoted by A ∪ B, is the set that contains all elements that are either in A or in B, or in both. 


Term

Definition
The _________ of a finite set
A, denoted A, is an integer that represents the number of elements of A. 


Term

Definition
The _________ of a set
S, denoted P(S), is the set of all possible subsets of S. 


Term

Definition
The _________ of sets
A and B, denoted by A − B, is the set that contains those elements that are in A but not in B. 


Term

Definition
The __________ of two sets
A and B, denoted A × B, is the set of all pairs (a, b) where a is an element from A and b is an element from B. 


Term

Definition
The ___________ of sets A and B, denoted by A ∩ B, is the set that contains all elements that are in both A and B. 


Term

Definition
We say that
a ≡b( mod m), a is congruent b modulo m, if a mod m = b mod m. 


Term

Definition
We say that the sets
A and B are ______ if A ∩B = ∅ 

