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August 2009Zero and the Number LineHow "Wide" Is Zero?We note that zero is often shown on number lines as occupying some width on the line. We often draw actual lines to represent zero on a line. This re-inforces the convention that zero is an actual number. But how wide is zero as a quantity? What dimensions does it have on a number line? In the chart below "Cats in our street" we chart a quantity (the number of cats) against ordinal values (the hours 0 to 23). This example demonstrates the difference between the use of zero as a quantity and as an ordinal number. Notice that that the ordinal hour "0" on the X axis has the same width as hour "1" or hour "2". On the Y axis, however, a zero quantity has no height - it occupies no length at all on the axis. As a quantity, zero occupies zero width on the line. Even a small increase in the "width" of zero in the positive or negative directions results in a non-zero. It must always be remembered that as a physical quantity zero has zero height, zero width and zero length. Any other representation, such as a dot or a line, is a human invention. When viewing zero as nothing, null or an empty set, we are not "taking zero off the number line" as it was never there to begin with.
Regards, AJ Corcoran
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