Natural Numbers (Counting Numbers): $\mathbb{N} = \{1, 2, 3, 4, 5, \dots\}$. There is no greatest natural number.
Whole Numbers: The collection of natural numbers along with zero: $\mathbb{W} = \{0, 1, 2, 3, 4, \dots\}$. Every natural number is a whole number, but $0$ is a whole number that is not a natural number.
- Predecessor: The number just before a given number: $\text{Predecessor of } n = n - 1$. (Note: In whole numbers, $0$ has no predecessor!).
- Successor: The number just after: $\text{Successor of } n = n + 1$.
Arithmetic on the Number Line
- Addition: Moving rightwards on the number line. (e.g. $3 + 4$: start at 3, take 4 steps to the right $\to 7$).
- Subtraction: Moving leftwards. (e.g. $7 - 4$: start at 7, take 4 steps to the left $\to 3$).
- Multiplication: Repeated steps of equal length to the right. (e.g. $3 \times 2$: start at 0, take 3 steps of 2 units $\to 6$).