Is zero an even number?

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Atlantic City

Superstorm Sandy had many consequences, some easier to foresee than others. Millions experienced floods and power cuts, the New York marathon was cancelled, and pictures of sharks in the city appeared on the internet. Another outcome was to draw attention to the unique position of the number zero.

To deal with fuel shortages after the storm, New York Mayor Michael Bloomberg introduced rationing on 8 November.

"Drivers in New York City who have licence plates that end in an odd number or end in a letter or other character will be able to gas or diesel only on odd-numbered days such as tomorrow which happens to be the 9th," he said.

"Those with licence plates ending in an even number, or the number zero, will be able to buy gas or diesel only on even number days such as Saturday November 10th."

The use of the phrase "even number, or the number zero" implies that zero is not even. On the other hand, the mayor is lumping zero together with the even numbers, so he certainly doesn't think it's odd.

So what is it - odd, even or neither?

Image caption,
This car was allowed to fill up on the last day of rationing - 23 November

For mathematicians the answer is easy: zero is an even number. The rest of us may not feel completely sure.

According to Dr James Grime of the Millennium Maths Project at Cambridge University, reaction time experiments in the 1990s revealed people are 10% slower at deciding whether zero is odd or even than other numbers.

Children find it particularly difficult to recognise if zero is odd or even. "A survey of primary school children in the 1990s showed that about 50% thought zero is even, about 20% thought it was odd and the remaining 30% thought it was neither, both, or that they don't know," explains Dr Grime.

"It appears that we may file numbers mentally into lists such as the even numbers two, four, six, eight or numbers to the power of two which would include two, four, six, eight or two, four, eight, 16. Zero is not on these lists so it takes us longer to work out."

So why, mathematically, is zero an even number? Because any number that can be divided by two to create another whole number is even. Zero passes this test because if you halve zero you get zero.

Zero also has odd numbers either side of it - minus one and one - and so this is another test it passes to be classified as an even number.

Image caption,
Police let cars into Paris every day, if their number plate ended in zero

In fact, there is an argument that zero is the most even number of all. A number which is "doubly even" can be divided by two and then divided by two again. Zero can be divided by two forever and the result will always be a whole number - zero.

It's not just the public who have struggled to recognise zero as an even number. During the smog in 1977 in Paris, car use was restricted so that people with licence plates ending in odd or even numbers drove on alternate days.

"The police did not know whether to stop the zero-numbered licence plates and so they just let them pass because they didn't know whether it was odd or even," says Dr Grime.

It even took mathematicians some time to agree on the question.

To begin with, zero was not recognised as a number at all. The Babylonians and the Ancient Greeks used it to differentiate between small and large numbers, for example 26 and 206. Before this, people could only tell if one number was bigger than another by the context in which it was used.

In the 13th Century, the Italian mathematician Fibonacci was the first to popularise Arabic numerals, the numbers that we use today, in Europe. He classified one to nine as numbers but zero as a "sign".

The struggle they had was if zero is nothing, is it even a number at all and can it have the properties of being a number? For example, oddness or evenness?

"It wasn't until the 1600s that zero was truly accepted as an even number - after resistance and debate," says Grime.

For more than 1,000 years mathematicians had difficulties with the number zero and non-mathematicians are still often uncertain about how to classify it.

So Bloomberg had every reason to spell out to New Yorkers in black and white that he was lumping zero along with the (other) even numbers.

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