Whole numbers are simply all the counting numbers and the number zero. You can always express any whole number as one or more digits, and without using a decimal point or a fraction. Whole numbers are all integers, but not all integers are whole numbers. This is because all whole numbers are positive (or zero) -- negative numbers are not whole numbers.
Integers include every whole number and its negative counterpart. For instance, 3 is a whole number, and -3 is its negative counterpart; both numbers are integers. Zero is also an integer, since all whole numbers are integers. As with whole numbers, you never need to use a decimal point or a fraction to express an integer.
A number line can help to illustrate mathematical scenarios or solve problems. A number line is especially useful in illustrating that positive integers all have negative counterparts, as every positive integer is exactly the same distance from zero on a number line as its negative counterpart. For instance, 4 is exactly the same distance from zero on a number line as -4.
In math, a "set" is a collection of numbers. A finite set includes a predetermined quantity of numbers. In set notation, sets are represented inside braces; for example, {2,3,4} is a set including only the integers 2, 3 and 4. Sets can also include an infinite amount of numbers. "Z" is used by mathematicians to represent the entire set of integers. Each number included in a set is called an "element" of that set, so every integer is an element of the set of integers Z.
Understanding integers is important to understand another set of numbers called "rational numbers." Any number that can be expressed as a fraction with integers as the denominator and the numerator is a rational number. Every integer, therefore, is a rational number, since every integer can be expressed as a fraction using only integers; for instance, 5 can also be expressed as 5/1. Conversely, then, 1/5 is also a rational number, although it is not an integer.