MA4601 Week 1
1 Functions
Lecture 1
1.1 Number Systems
Natural numbers N are the set of positive whole numbers:
0, 1, 2, 3, 4, .... ∈ N.
Note, 0 is not always included in the set of natural numbers.
Integers Z are the set of whole numbers:
..., −3, −2, −1, 0, 1, 2, 3, , .... ∈ Z.
N is a subset of Z: N ⊆ Z.
Rational numbers Q include fractions with integer numerators and denomina-
tors:
1 3 12
,− , ,
2 4 5
are all examples of rational numbers. Once again, Z ⊆ Q.
Real numbers R include decimals and irrational numbers (eg. π).
√
0.3333..., π = 3.14159....., 2 = 1.4142...
are all examples√of real numbers. The first can be written as a rational num-
ber: 1/3. π and 2 are known as irrational numbers.
Complex numbers C include the square root of negative numbers:
√
i = −1.
Questions will usually state what set to use. If in real numbers R and asked to
get the cube root, there is only one solution. If in set of complex numbers C,
then there are three solutions.
1
1 Functions
Lecture 1
1.1 Number Systems
Natural numbers N are the set of positive whole numbers:
0, 1, 2, 3, 4, .... ∈ N.
Note, 0 is not always included in the set of natural numbers.
Integers Z are the set of whole numbers:
..., −3, −2, −1, 0, 1, 2, 3, , .... ∈ Z.
N is a subset of Z: N ⊆ Z.
Rational numbers Q include fractions with integer numerators and denomina-
tors:
1 3 12
,− , ,
2 4 5
are all examples of rational numbers. Once again, Z ⊆ Q.
Real numbers R include decimals and irrational numbers (eg. π).
√
0.3333..., π = 3.14159....., 2 = 1.4142...
are all examples√of real numbers. The first can be written as a rational num-
ber: 1/3. π and 2 are known as irrational numbers.
Complex numbers C include the square root of negative numbers:
√
i = −1.
Questions will usually state what set to use. If in real numbers R and asked to
get the cube root, there is only one solution. If in set of complex numbers C,
then there are three solutions.
1
