1) A SET is a collection of distinct elements or objects. SETS are enclosed within BRACES { } and must have COMMAS between each element.
2) An EMPTY SET or NULL SET is a set with no elements. Symbols: { } or ∅.
Six Important Sets:
1) The REAL NUMBER SYSTEM is what we use in middle school math.
2) The set of COUNTING NUMBERS or NATURAL NUMBERS are made up of the elements {1, 2, 3, 4, ...}. This set is made up of only POSITIVE NUMBERS.
3) The set of WHOLE NUMBERS is formed when you add the element of ZERO to the set of COUNTING NUMBERS to form {0, 1, 2, ...}.
4) The set of INTEGERS are similarly formed by adding NEGATIVE NUMBERS to the set of WHOLE NUMBERS to form {..., -2, -1, 0, 1, 2, ...}.
5) The set of RATIONAL NUMBERS is made up of any number that can be expressed as any of the three types of number below:
1. FRACTIONS ex. a/b, where a & b are INTEGERS or
2. TERMINATING DECIMALS (END) ex. 1.5 or
3. REPEATING DECIMALS ex. 0.2̅
6) The set of IRRATIONAL NUMBERS is the opposite of RATIONAL NUMBERS. Therefore these numbers cannot be expressed as:
1. FRACTIONS or
2. TERMINATING DECIMALS or
3. REPEATING DECIMALS ex. π, √2, π/3
* A number can belong to ONE or MULTIPLE different sets of numbers. For example, the number 4 is a counting number, a whole number, an integer and a rational number.
Parent Tip: Review the logic above to help your child master the concept of the number system worksheet.
