Whole Numbers - The Number Line

Whole numbers consist of the number $0$ and all natural numbers ($1, 2, 3, \dots$). On a number line, this collection starts from a point marked $0$ and extends infinitely to the right, often represented by a horizontal line with an arrow at the right end.

The number line is constructed by marking a starting point as $0$ and then marking points to its right at equal intervals. This equal gap between any two consecutive whole numbers is called a 'unit distance'. Visually, it looks like a ruler with points $0, 1, 2, 3, \dots$ spaced evenly.

On the number line, for any two whole numbers, the number that lies to the right is the greater number. For example, since $7$ lies to the right of $4$, we say $7 > 4$. Conversely, the number on the left is always smaller.

Addition on the number line is performed by moving to the right. To calculate $a + b$, you start at the point $a$ and make $b$ jumps of one unit each to the right. The point where you land is the sum. Visually, this is depicted as a series of forward-moving arcs.

Subtraction on the number line involves moving to the left. To find $a - b$, you start at the point $a$ and move $b$ units toward the left (toward $0$). This is represented by backward-moving jumps or arrows pointing left. Note that for whole numbers, we can only subtract a smaller number from a larger one or equal one.

Multiplication is represented as repeated addition starting from $0$. To find $a \times b$, you start at $0$ and make $a$ jumps, where each jump covers a distance of $b$ units. For example, $2 \times 3$ is visualized as two large leaps of $3$ units each, landing on $6$.

Every whole number has a successor, which is the number obtained by adding $1$ and is located exactly one unit to the right. Every whole number except $0$ has a predecessor, which is the number obtained by subtracting $1$ and is located exactly one unit to the left.