Mathematics For Computer Science - Notation for Sets

​…	​An ellipsis is used to show a regular sequence. {1, 2, 3, …, 100} is the set of all natural numbers between 1 and 100. The ellipsis shows that all numbers in between 3 and 100 are also included.
​|	​‘Such that’. This is used as a separator with the variable to the left and the rule to the right.
​∈	​‘is a member of’. x ∈ ℕ means that x is a member of the set of natural numbers.
​∧	​‘AND’. x > 7 ∧ x < 10 means x is greater than 7 and x is less than 10.

​​Notation for sets
In the previous section, sets have been discussed without explicitly discussing what one
is. A set is an unordered collection of values in which each value occurs at most once.
Curly braces { } are used to define a set, such as A = {5, 6, 7, 8, 9}. An empty set (one
with no elements) can either be shown using { } or using the symbol Ø.
Table on the left shows other symbols that are used for set comprehension and Symbol Explanation
For example, A = {x | x ∈ ℕ ∧ x < 6} would be read as ‘x, such that x is a member of
the set of natural numbers and x is less than 6’. In this example, A = {0, 1, 2, 3, 4, 5}.
If needed, the variable to the left of the separator can be replaced by a term (such as 2x,
or 2x + 1). If B = {2x | x ∈ ℕ} then B is {0, 2, 4, 6,…}, the set of all even natural numbers.
If C = {2x + 1 | x ∈ ℕ ∧ x < 4} then C is {1, 3, 5, 7}, the set of all odd natural numbers
2x + 1, where x < 4.