The Number System

Not Real Numbers

-Any number that is not Natural, Whole, Integer, Rational, or Irrational. -Examples: Square Root of any negative number Complex Numbers (3 + 9i) -Note: If you try to take the square root of a negative on your calculator, it should say "Error" (unless you have a fancy calculator).

Real Numbers

-The set of all numbers that are Natural, Whole, Integers, Rational, Or Irrational.

Integers

Example: ...-4, -3, -2, -1, 0, 1, 2, 3, 4... -All whole numbers and their opposites -Positive & Negative -Still no Fractions or Decimals -All NATURAL and WHOLE numbers are ALSO Integers

Whole Numbers

Example: 0, 1, 2, 3, 4, 5... -All of the Natural Numbers, but with Zero Included -No negatives -No Fractions or Decimals -All NATURAL numbers are ALSO Whole Numbers

Natural Numbers

Example: 1, 2, 3, 4, 5,... -All positive numbers (no negatives allowed!) -No Zero -No Fractions or Decimals -These are the numbers you first learned as a child.

Rational Numbers

Examples: 3, -5, 2.5, -8.1, 2/3, -8 1/2, 4.3333... -Any number that can be written as a fraction a/b, where a and b are integers -Positive and Negatives -Includes almost all fractions (unless they have a square root) -Includes all decimals that either terminate or have a repeating pattern -All NATURAL, WHOLE, and INTEGERS are ALSO Rational

Irrational Numbers

Examples: Square Root of 2, pi, Square Root of 7 -Any number that cannot be written as a fraction -Every square root is irrational, except those that are perfect squares -Decimals that never terminate and do NOT have a repeating pattern. -Natural, Whole, Integers, and Rationals are NEVER Irrational