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14 THE FASCINATION OF NUMBERS

possess if they are all empty. There is nothing in any one
bucket and there is nothing in all of them taken collectively.

For a long time negative numbers were suspect and re-
jected as having no relation to physical life. If numbers are
used to represent tangible objects such as, for instance,
strawberries, it might be argued that you cannot have a
negative number if you cannot also have a negative straw-
berry. One might as well ask how one is to eat a negative
strawberry, but if the analogy is not too strained, it may be
said that a negative strawberry is one which has been taken
by somebody else and which has probably already been
eaten.

The relationship between positive and negative numbers
may be more easily understood if they are considered in
terms of increments of addition and deduction respectively.
As a business firm prospers, so its capital increases by the
addition of profits; that is, by the addition of positive num-
bers to the number representing the size of the capital.
When losses are incurred, however, the capital number is
reduced by the addition of negative numbers. It may be
argued that this is only another way of taking away the
positive numbers we have previously added, but what is the
position when the capital itself becomes a negative quantity?

For example, where the capital has reached the depths of
minus £1000 (meaning in essence that this amount is owed
to other people) how, if a further loss accrues, is one to deduct
a positive quantity from this amount? It is far more logical to
add a negative quantity and the final result is clearly the
same.

Just as the realm of numbers may be separated into two
divisions differentiating between positive and negative num-
bers, so may each of these divisions be subdivided into the
categories of integral numbers and fractional numbers. An
integral number is a synonym for a whole number, whereas
a fractional number, as its name implies, is one expressed as
a fraction.

We thus have four distinct categories of what are known as