The Other Side of Zero - Explorations with Integers

Integers are a collection of numbers formed by whole numbers ($\{0, 1, 2, 3, ...\}$) and the negatives of natural numbers ($\{-1, -2, -3, ...\}$).

On a number line, numbers to the right of $0$ are positive integers, and numbers to the left of $0$ are negative integers.

The number $0$ is an integer that is neither positive nor negative.

For any two integers on a number line, the integer occurring to the right is always greater than the integer occurring to the left. Thus, every positive integer is greater than every negative integer.

The Absolute Value (or modulus) of an integer $a$, denoted by $|a|$, is its numerical value without regard to its sign. For example, $|-5| = 5$ and $|5| = 5$.

The Additive Inverse of an integer $a$ is $-a$, such that $a + (-a) = 0$.

To add two integers with the same sign, add their absolute values and place the common sign before the sum.

To add two integers with different signs, find the difference between their absolute values and place the sign of the integer with the larger absolute value before the result.

Subtraction of an integer is the same as adding its additive inverse. For any two integers $a$ and $b$, $a - b = a + (-b)$.