You know how your phone has different group chats? One for family, one for class, one for your cricket team. Each group is a collection of specific people. That’s literally what a set is in math — a collection of things.
What a set actually is
A set is a well-defined collection of distinct objects. We write it with curly braces:
Three things to notice:
- Elements separated by commas
- Inside curly braces
- The set has a name (capital letter), here
Set-builder notation — when listing is annoying
What if you want the set of all even numbers? You can’t list them all. So we describe the rule instead:
Read this as: “B is the set of all x such that x is even.”
A shortcut for reading this
The vertical bar just means “such that.” So is always “the set of all x such that [rule].”
Try it yourself
Write the set of all prime numbers less than 10.
Solution
Why not 1? Because 1 is not prime (a prime has exactly two different divisors: 1 and itself).
Common mistakes
- Writing elements more than once. is just . Sets don’t count duplicates.
- Confusing set-builder notation with a function.
- Forgetting that order doesn’t matter. .
Next up
types-of-sets — empty sets, finite vs infinite, and why mathematicians invented the empty set on purpose.