Is it true the set of whole numbers includes zero but the natural numbers do not?

Answer 1

There really isn't a uniform, generally accepted, definition for "whole numbers", or even for "natural numbers".

Traditionally, "natural numbers" means {1, 2, 3, ...}. However, more recently, it was seen convenient to include zero, so "natural numbers" would mean the set {0, 1, 2, 3, ...}.

In the case of "whole numbers", the situation is even worse; some define it to include not only zero, but also negative numbers. Others don't include negative numbers.

Suggestion: When you need to avoid confusion, use non-ambiguous names such as:

* "Integers" for {... -3, -2, -1, 0, 1, 2, 3, ...}

* "Positive integers" for {1, 2, 3, ...}

* "Non-negative integers" for {0, 1, 2, 3, ...}