Question

describe the relationship between whole numbers and integers and negative numbers

Answer 1

Briefly:

- Whole numbers are the nonnegative integers: 0, 1, 2, 3, ... (some texts call these natural numbers; others reserve “natural” for 1,2,3,...).
- Integers are all whole numbers plus their negatives: ..., −3, −2, −1, 0, 1, 2, 3, ...
- Negative numbers are numbers less than zero. In the context of integers they are the negative integers (−1, −2, −3, ...), but “negative numbers” can also refer to negative fractions or decimals.

Key relationships:
- Every whole number is an integer (whole numbers ⊂ integers).
- Negative integers are integers but not whole numbers.
- 0 is both a whole number and an integer, and it is neither positive nor negative.
- On a number line, whole numbers sit at 0 and to the right; integers extend both left (negatives) and right.
- Algebraically: integers are closed under addition, subtraction and multiplication; whole numbers are not closed under subtraction (e.g., 2 − 5 is not a whole number).