4-1 Represent Integers

Property

Integers are the set of whole numbers and their opposites: $\{..., -3, -2, -1, 0, 1, 2, 3, ...\}$

Zero is neither positive nor negative.

Property

Positive integers can be written with or without a positive sign: $+5 = 5$.
Negative integers must always be written with a negative sign: $-3$.
Zero is written without any sign: $0$.

Examples

Property

We can use negative numbers to indicate a decrease or a loss, and positive numbers to indicate an increase or a gain.
An increase or decrease is called a net change.

Examples

• If the temperature was $8^{\circ}$ and changed by $-12^{\circ}$, the new temperature is $-4^{\circ}$.
• A stock was worth 25 dollars per share and is now worth 18 dollars. The net change in value is $-7$ dollars.
• Corinne's bank account had 150 dollars, and she wrote a check for 200 dollars. Her account's value changed by $-200$ dollars, resulting in a balance of $-50$ dollars.

Explanation

Signed numbers are perfect for showing change. A positive number shows a gain or increase, like the temperature rising. A negative number shows a loss or decrease, like a stock price dropping. This is the 'net change.'