Integers consist of the counting numbers, their negative counterparts and zero. Mathematically, the set of integers is denoted {..., -2, -1, 0, 1, 2, ...}, where the successive dots signify that the numbers never end, continuing to positive infinity on the right and negative infinity on the left. Integers don't include fractional or decimal parts -- for instance, -3 and 4 are integers, but 2/5 and 0.3 aren't integers.
Signed numbers are those preceded by a "+" or "--" sign. Generally, the counting numbers are written without a "+" sign, as they are assumed to be positive. It's perfectly acceptable to include the "+" sign in front of the counting numbers -- for example, 3 and +3 are equivalent -- but this sign is usually omitted for the sake of simplicity. Likewise, zero typically appears without a sign in front of it, although it is permissible to include either a "+" or "--" sign. Negative numbers, however, are always preceded by a "--" sign. Any number written with a sign in front of it is considered a signed number. Negative numbers are always signed, while positive numbers and zero typically are unsigned.
Teachers often use number lines when introducing signed and unsigned integers. A number line is a horizontal line with arrows on each end, in which zero typically appears in the middle, the positive integers appear in ascending order on the right and the negative integers appear in descending order on the left. The positive, or counting, integers may be written either signed or unsigned, while negative integers are always signed. Two integers that lie the same distance from zero but on opposing sides of the number line are known as opposites. For instance, 7 and -7 are opposites, as they both sit seven units from zero.
When adding two unsigned integers, such as 0 + 3, the answer will always be zero or greater. When subtracting two unsigned integers, such as 5 -- 3 or 3 -- 5, the answer may be either positive, negative or zero. If adding a signed negative integer to another signed negative integer, as in -8 + -7, the answer will always be a signed negative integer, -15 in this case. Multiplying or dividing two unsigned integers will always produce a positive integer or zero -- for example, 6*3 = 18. Multiplying or dividing two signed negative integers also always results in a positive integer; -6*-3 = 18. However, multiplying or dividing a signed negative integer by a positive integer always produces a signed negative integer, as in -6*3 = -18 or 6*-3 = -18.