How are sets written using braces in mathematics?

In set theory, sets are commonly represented using braces {} in two primary ways:

• Listing members: For finite sets, you can list all members enclosed in braces. For example, the set containing the numbers 1, 3, 5, 7, and 9 is written as {1, 3, 5, 7, 9}.1
• Specifying conditions: For sets that are infinite or too large to list, you can use a formula or condition that defines the members. This is often written in the form {x : α}, where x is the variable and α is the condition that must be satisfied. For example, {x : x is a prime number} represents the set of all prime numbers.2

When using a formula to generate elements, a vertical bar is often used to mean "such that." For instance, {2x | x = 1, 2, 3, ...} represents the set of positive even numbers.1