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Zero is an even number, not odd. An integer is even if it is a multiple of 2, and 0 = 2 × 0, so zero divides by 2 with no remainder. It also sits between two odd numbers (−1 and 1) on the number line and obeys every parity rule, such as even + even = even.
Around the turn of the millennium, newspapers made a fuss over a curious calendar quirk: written as 2000/02/02, February 2, 2000 was the first date in ages whose every digit was even. Write out 2002/02/02 a couple of years later and you get the same all-even spread. However, some readers were incredulous, for while they were sure that the number 2 was even (the very torch we use to illuminate other even numbers), they weren’t so sure about the “number” 0.
In a survey of nearly 400 seven-year-old children, about 45% of them agreed that the number 0 is, in fact, even. However, when their options were expanded to “neither odd nor even”, “both odd and even” and simply “don’t know”, doubt seeped in and they reconsidered their answers. The share of children calling it even slipped to 32%. So, what then is 0… odd or even?
Technically, It’s Even
Since their inception, the distinct nature of numbers was leveraged by traders to count units of a commodity and the money it cost them. A cow or a piece of silk would be sold for some certain amount of countable shillings, but how could traders incorporate the absurd concept of zero in their transactions? How could you buy nothing? Perhaps at the cost of nothing?
This inscrutable concept exists only in abstraction, which, as some argue, doesn’t make it any different from every other number. Believed to be one of the most important discoveries in mankind’s history, it was a huge cause of discomfort initially, since it is neither negative nor positive. There was no unanimity in deciding its parity, whether it was even or odd. However, it seems to pass every test that an even number must pass to prove its even-ness. So, technically, it is even. In fact, it is the most even number there is.
The very first test that comes to mind is to check whether the number is divisible by or a multiple of 2. In the past, mathematicians ascribed every even number with a degree of even-ness, which they determined by counting the number of times it could be successively divided by 2.
For instance, 14 can be divided only once for the successive number (7) isn’t divisible by 2. This is called a single-even. On the other hand, 12 can be divided twice, a double-even, while 24 can be split thrice, a triple-even. However, zero can be divided interminably, for when zero is divided by two, the result is again zero, which when divided by two is zero once again, a sequence that repeats forever. The calculation requires us to divide nothing or zero objects into two equal halves of nothing, which can be further divided into four equal halves of nothing or zero objects and so on.
14 ÷ 2 = 7
12 ÷ 2 = 6 ÷ 2 = 3
24 ÷ 2 = 12 ÷ 2 = 6 ÷ 2 = 3
0 ÷ 2 = 0 ÷ 2 = 0 ÷ 2 = …
One can also examine whether zero obeys certain fundamental arithmetic rules. For instance, the sum of two even numbers must be an even number, which is true for zero, as the sum of zero and an even number is equal to the very number added to zero, an even number. Furthermore, the sum of an odd number and an even number must be an odd number, a rule that zero also obeys, as zero added to an odd number will obviously equal the very odd number added to it! Absurd, perhaps inane, but consistent and logical, the only meritorious qualities in mathematics.
Perhaps an even simpler way is to check its position on the number line. Even and odd numbers alternate, so an even number always sits sandwiched between two odd numbers, and an odd number between two even ones. Zero, as everyone hopefully knows, lies between −1 and 1 (both odd), which lands it squarely in the even camp.
Why Do So Many People Hesitate To Call Zero Even?
If the case is so airtight, why does zero still trip up so many otherwise confident counters? The doubt we saw in those seven-year-olds, who happily called zero even until handed the escape hatch of “neither”, is not just playground confusion. Grown-ups fare little better. In studies of undergraduates and trainee teachers, people could correctly apply the definition of even to zero, yet still felt unconvinced, because the answer clashed with their mental picture of what an even number “should” look like.
The hesitation even shows up in our reflexes. In reaction-time experiments pioneered by the cognitive scientist Stanislas Dehaene, subjects asked to sort flashed numerals as odd or even were measurably slower with zero than with 2, 4 or 6, lagging by as much as 60 milliseconds, roughly a tenth of the average response. People know zero is even; their gut just has not quite caught up. So the doubt is not really a failure of arithmetic, but a quirk of how our minds file the number that stands for nothing.
Where Does Zero’s Parity Actually Matter?
This might sound like a question with nowhere to live but a classroom, yet zero’s parity has occasionally spilled into the real world, sometimes awkwardly. During an odd-even driving restriction in Paris in 1977, when cars could use the roads on alternate days depending on the last digit of their number plates, the police reportedly let drivers whose plates ended in 0 off the hook on odd-only days, simply because the officers were not sure whether 0 counted as even. The mathematics was settled; the enforcement was not.
To head off exactly that kind of confusion, some lawmakers have spelled it out. A Maryland statute governing its own odd-even scheme flatly declares that “zero is an even number”, turning a point of arithmetic into a point of law. The same convention is baked into the standardized tests that gatekeep graduate study: the official guides for both the GMAT and the GRE state plainly that 0 is even, so anyone treating it otherwise on test day is simply marked wrong. Far from a trivial curiosity, then, zero’s membership in the even club is something traffic officers, legislators and exam boards have all had to commit to in writing.
