Describe the Structure of the Real Number System, Defining Each Type of Number which It Comprises and Making Clear the Relationship between Them

The first numbers that we are introduced to from an early age are 1, 2, 3, 4 etc.
These are called the 'Natural numbers', and can be placed on a number line from 1
to infinity. The natural numbers, in order, are always 1 whole number larger or
smaller than the next.
When we add or subtract the natural numbers the answer is always a natural
number. If we use subtraction or division however, we would without any other
system, not always be able to obtain an answer within the natural number system.
The sum 8 minus 10 for example would be impossible therefore a new number
system is needed. Suggate (1998, p.40) uses temperatures below freezing as an
example. In this instance we record how many degrees below O°c it is by counting
backwards from 0, to the left, using the 'negative' numbers. The integers are all
positive and negative whole numbers including 0 but the positive integers are also
natural numbers.
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