Integers - Introduction to Integers

Integers are a collection of numbers that include all whole numbers ($0, 1, 2, 3 \dots$) and their negative counterparts ($-1, -2, -3 \dots$). Visually, you can imagine a set where the right side contains positive numbers, the left side contains negative numbers, and zero sits exactly in the middle.

The Number Line is a horizontal straight line used to represent integers. Zero ($0$) is the origin or center point. Positive integers are marked at equal intervals to the right of zero, and negative integers are marked at equal intervals to the left of zero. As you move from left to right, the value of the integers increases.

Positive integers are numbers greater than zero ($> 0$), often written with a plus sign ($+$) or no sign at all. Negative integers are numbers less than zero ($< 0$) and must always be written with a minus sign ($-$). Zero is a unique integer that is neither positive nor negative.

In the comparison of integers, any positive integer is always greater than any negative integer. On the number line, for any two integers, the one appearing to the right is always greater. For example, $-1 > -5$ because $-1$ is to the right of $-5$. Zero is smaller than every positive integer but larger than every negative integer.

The Successor of an integer is the number that comes immediately after it (one unit to the right on the number line), calculated by adding $1$. The Predecessor is the number that comes immediately before it (one unit to the left on the number line), calculated by subtracting $1$. For example, the successor of $-2$ is $-1$ and the predecessor is $-3$.

The Absolute Value of an integer is its numerical distance from zero on the number line, regardless of the direction. It is denoted by vertical bars $|x|$ and is always non-negative. For example, both $|5|$ and $|-5|$ equal $5$ because both are exactly $5$ units away from zero.

Addition of integers on a number line follows specific movement rules: to add a positive integer, move to the right; to add a negative integer, move to the left. For example, to solve $2 + (-3)$, start at $2$ and jump $3$ units to the left to land on $-1$.