Why do we need more numbers? As you know, 3 – 3 = 0 (zero). Mathematicians had debated for centuries whether or not zero (0) was actually a number. What about 3 – 5? Such an operation would bring you to the left of 0 on the number line. It was therefore obvious that a whole new group of numbers had to be invented to deal with this new situation.
–3 –2 –1 0123 Using the number line: 3 – 5 = −2
The set consisting of all positive and negative whole numbers is known as the set of integers. This set is denoted by the symbol Z.
Z = {..., −3, −2, −1, 0, 1, 2, 3, ...} Integers are whole numbers (positive and negative) and zero.
KEY TERM
The natural counting numbers are part of this set of integers. Numbers increase in size as you go from left to right on the number line.
2 is greater than −3 (2 > −3) 0 is less than 4 (0 < 4)
Integer operations
Operation 1: Combining (addition and subtraction) Same sign:
+3 + 5 = +8 [Adding two positive numbers] –3 – 5 = −8 [Adding two negative numbers] Different signs:
+3 – 5 = −2 [Take the numbers away. The sign of the answer is the sign of the bigger number.]
−7 + 12 = +5 +4 – (+2) = +4 – 2 = 2
[A negative sign outside the bracket changes the sign inside the bracket.]
