Numbers of Algebra 3The set consisting of the whole numbers and their opposites is the set of
integers (usually denoted Z):Z = (^) {}...,,,−,,,−−−,,, ,,,,, ...
The integers are either positive ( 12 ,,, 233 ...), negative
(...,,,− 321 ,,,−−− ), or 0.
Positive numbers are located to
the right of 0 on the number line, and
negative numbers are to the left of 0, as
shown in Figure 1.5.
Problem Find the opposite of the given number.
a. 8
b. −
Solution
a. 8
Step 1. 8 is 8 units to the right of 0. The opposite of 8 is 8 units to the left
of 0.
Step 2. The number that is 8 units to the left of 0 is − 8. Therefore, − 8 is the
opposite of 8.
b. −
Step 1.− 4 is 4 units to the left of 0. The opposite of − 4 is 4 units to the right
of 0.
0 is neither positive nor
negative.
It is not necessary to write a + sign on positive
numbers (although it’s not wrong to do so). If
no sign is written, then you know the number
is positive.
Figure 1.4 Whole numbers and their opposites
–6 –5 –4 –3 –2 –1 041 2 3 5 6
Figure 1.5 Integers
–5 5
Zero
Negative Integers ↓↓ Positive Integers
–6 –4 –3 –2 –1 041 2 3 6