Here are some definitions for sets of numbers you may wish to utilize when having your students work with sets.
Yes, these are real definitions.

Numbers Definition Sample
Perfect numbers - numbers whose divisors add up to the number itself. (Do not consider the number itself as one of the divisors.)  6 = 1 + 2 + 3
so 6 is a perfect number.
Deficient numbers - numbers whose divisors add up to a value less than the number itself.  (Do not consider the number itself as one of the divisors.) 9 is a deficient number.
1 + 3 = 4
Abundant numbers - numbers whose divisors add up to more than the number itself. (Do not consider the number itself as one of the divisors.) 12 is an abundant number:
1 + 2 + 3 + 4 + 6 = 16
Figurative numbers - numbers that represent the number of objects needed to form geometrical objects such as triangles, squares, pentagons, etc.
Triangular numbers - a number representing the number of objects that can be used to form a triangle.  •      1 is a triangular number
          
 •
• •      3 is a triangular number
  •
 • •
• • •    6 is a triangular number
Square numbers - a number representing the number of objects that can be used to form a square.
 
  •      1 is a square number
 
  • •
  • •     4 is a square number
  • • •
  • • •
  • • •    9 is a square number