Integers & Rational Numbers

Integers: Whole numbers and their opposites: $\ldots, -3, -2, -1, 0, 1, 2, 3, \ldots$ The set of integers is denoted by $\mathbb{Z}$.

Positive integers: Numbers greater than 0: $1, 2, 3, 4, \ldots$. These are also called natural numbers or counting numbers.

Negative integers: Numbers less than 0: $-1, -2, -3, -4, \ldots$. The negative sign indicates direction (left of zero on number line).

Zero: Neither positive nor negative. It's the reference point on the number line and the additive identity ($a + 0 = a$ for any number $a$).

Number line: Visual representation where numbers increase to the right and decrease to the left. Zero is in the middle, positive numbers extend right, negative numbers extend left.

Opposites: Two numbers that are the same distance from zero but on opposite sides. $5$ and $-5$ are opposites. The opposite of $-3$ is $3$.

Real-world examples: Temperature ($-5°C$ below freezing), elevation ($-50 \text{ m}$ below sea level), debt ($-\$100$), gains and losses.