Definition
Solution set
A solution set is the set containing every value or object that satisfies a condition.
Continue from this idea into connected AXIO math.
All that works, and only what works.
Boundary: A solution set can have no members, one member, many members, or infinitely many members.
What it means
Finding one answer is not enough when several answers work. The solution set gathers every answer that passes the test, leaves out every answer that fails, and treats the finished collection as a set.
Remember it
All that works, and only what works.
Example
For whole numbers x with 1 < x ≤ 5, the solution set is {2, 3, 4, 5}. Each listed number fits both inequalities, and no other whole number does.
Watch for
A solution set can have no members, one member, many members, or infinitely many members.
Common mix-up
A single solution is one member; the solution set is the complete collection.
Exact meaning
The solution set of a mathematical statement or system is the set of all and only the values, objects, or assignments that make every required condition true. It may be empty, finite, or infinite.