Integers are whole numbers, both positive and negative including zero.
Integers do not have a fractional part (e.g. doesn’t have anything after the decimal point, another way of saying that they are whole numbers).
Example: the numbers \(1\), \(5\), \(0\), and \(-234\), are all integers, but the numbers \(2.3\), \(\tfrac{4}{5}\), \(-\tfrac{3}{11}\) are not integers.
Integers can be grouped together into a set. We call this as the set of integers, labelled as \(\mathbb{Z}\) for the German word Zahlen meaning “numbers”.
\[\mathbb{Z} = \{\dotsc, -4, -3, -2, -1, 0, 1, 2, 3, 4, \dotsc\}.\]
If a number, \(x\), is an integer, then \(x \in \mathbb{Z}\). For example, \(-4 \in \mathbb{Z}\) because negative four is an integer.
If \(x\) is not an integer, then \(x \notin \mathbb{Z}\). For example, \(\tfrac{1}{3}\notin\mathbb{Z}\) because a third is not a whole number. Also, \(\text{donkey}\notin\mathbb{Z}\) because a donkey is not even a number!