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

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).  

A function

f is called a _________________ if f is both one-to-one and onto (both injective and surjective).

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.

A function defined on a subset of real numbers is called

________ if for any x < y we have that f (x) ≤f (y).

A function defined on a subset of real numbers is called 

__________ if for any x < y we have that f(x) ≥ f(y).

A set

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

x

∈ B.

A _________ is a rule that associates to every element in a set

A (called domain), a single element in a set B (called range).

A _____________ is a sequence:

a, a · r , a · r², ..., a · rⁿ, ...where a is called the initial term and r is called the common ratio.

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

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.

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.

Let

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

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

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)).

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

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

Let b

> 1 an integer. Then any positive integer n can be uniquely expressed as:

n

= a_k⋅b^k + a_k-1⋅b^k-1+ ...+ a2⋅b²+ a1⋅b + a0

where k ≥

0 and ak, a1, a0 are all nonnegative integers smaller than b.

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.

The _________ of a finite set

A, denoted |A|, is an integer that represents the number of elements of A.

The _________ of a set

S, denoted P(S), is the set of all possible subsets of S.

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.

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.

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

We say that

a ≡b( mod m), a is congruent b modulo m, if a mod m = b mod m.

We say that the sets

A and B are ______ if A ∩B = ∅