The set of natural numbers are also called integers—or counting or whole numbers— which are usually defined as the positive and negative whole numbers, along with zero (0). But many times, mathematicians do not use the term “natural numbers,” and instead define numbers based on the following terminology and/or symbols:

**Group** |
**Name** |
**Symbol** |

…,-3,-2,-1, 0, 1, 2, 3… |
integers |
Z (after the German word *Zahl,* for “number”) |

1, 2, 3… |
positive integers (or often referred to as natural numbers) |
Z+ or N |

-1, -2, -3… |
negative integers |
Z- |

0, 1, 2, 3 … |
nonnegative integers (or often referred to as whole numbers) |
Z* (Z-star) |

0, -1, -2, -3 … |
nonpositive integers |
(no symbol) |