Lesson 2: Comparing and Ordering Integers

Property

For any two integers $a$ and $b$:

• $a < b$ means "$a$ is less than $b$."
• $a \leq b$ means "$a$ is less than or equal to $b$."
• $a > b$ means "$a$ is greater than $b$."
• $a \geq b$ means "$a$ is greater than or equal to $b$."

On a number line, $a < b$ means that $a$ lies to the left of $b$, and $a > b$ means that $a$ lies to the right of $b$.

Property

Integers are ordered on the number line: we say integer $a$ is less than integer $b$, and write $a < b$, whenever $b$ is to the right of $a$ on the number line.
This is the same as saying that $a$ is to the left of $b$. Given two integers $a$ and $b$, one of these statements is true: $a = b$, $a < b$, or $a > b$.

Examples

Property

On a vertical number line, integers positioned higher are greater than integers positioned lower.
If integer $a$ is above integer $b$ on a vertical number line, then $a > b$.
If integer $a$ is below integer $b$ on a vertical number line, then $a < b$.

Examples