Is zero a number? Many people feel that it isn’t really a proper number; not like one, two or three. It’s just nothing. A group of trainees was given a table showing the numbers of children in a class with birthdays in each month and asked which month had the smallest number of birthdays. Some of them had great difficulty in accepting that the month without any birthdays had the smallest number, because they did not think of zero as a number. So, is zero a number?

Part of the problem with zero is that it’s not uncommon for the word ‘nothing’ to be used for the symbol 0. This fixation on the idea that zero is nothing is, of course, a consequence of the over-emphasis on the cardinal aspect of number. If you have a set of zero objects in your hand then, of course, you do actually have nothing in your hand. But is zero nothing more than nothing? We have already seen that the cardinal view of a number is very limited. Once we consider the ordinal aspect, zero (as a label on the number line, for example) has at least the same status as any other number. In fact, it becomes a very significant and important number. It is the point before 1 on the number line, and sometimes the starting point; it is the point on the number line that separates positive numbers from negative numbers; it is the ground floor in the department store; it is midnight on my digital watch; it is freezing point on the thermometer.

A line of pegs in a classroom is labelled like a number line; there is a bag hanging on each peg, the bag on peg 1 containing one block, that on peg 2 containing two blocks, and so on. The photograph shows the peg labelled 0 and, hanging on this peg, there is an empty bag. This is a bag containing zero blocks. Here we see the two ideas of zero coming together: the position labelled zero (an ordinal zero) and the accompanying bag with nothing in it (a cardinal zero).

So, understanding the concept of zero involves connecting the symbol and the language, not just with ‘nothing’, an ‘absence of something’ and empty sets, but also with ordinal pictures of number where zero is very definitely something. When asked is zero a number, teachers added some insightful comments on this special number:

  • The problem is that we sometimes call it zero, we sometimes call it nought, and sometimes nothing. Other numbers like 1 have only one name.
  • When children do take-away questions and get nothing left, they tend to say ‘nothing’, but when they count backwards they always say ‘zero’ at the end, like a countdown for a spaceship.
  • Counting down is very clearly an ordinal aspect of number, isn’t it?
  • Do books have a page numbered zero?
  • I’m not sure, is zero a number?

Ask yourself: is zero a number? Make a list of situations in your everyday life in which you come across the symbol for zero (0). Compare your list with that of a colleague. In each example you come up with, discuss how or why the symbol is being used, what language goes with it, what it means in that context, and any other questions that might occur to you or puzzle you. Try to come up with some examples that are very different in the way the symbol is used.