Definition
Set
A set is a clearly described collection in which each object either belongs or does not belong.
Continue from this idea into connected AXIO math.
A set is like a club with a clear rule for who is in.
Boundary: “Some nice numbers” is not a clear set description unless “nice” is given an exact rule.
What it means
Think of a set as a collection with a clear membership rule. The rule lets you decide whether any object is in or out. You can describe a set by listing its elements in braces or by stating the rule they follow.
Remember it
A set is like a club with a clear rule for who is in.
Example
Let A be the set of positive even numbers less than 9. Then A = {2, 4, 6, 8}. Writing {8, 6, 4, 2, 2} names the same set because order and repeats do not create new elements.
Watch for
“Some nice numbers” is not a clear set description unless “nice” is given an exact rule.
Common mix-up
A set is not changed by rearranging its elements; a sequence can be changed by rearranging its terms.
Exact meaning
A set is a well-defined collection of distinct objects, called elements. An object either belongs to the set or does not; changing the listing order or repeating an element does not change the set.