Parity of Zero - Everyday Contexts

Everyday Contexts

Some of the contexts where the parity of zero makes an appearance are purely rhetorical:

• It provides material for Internet message boards and ask-the-expert websites.
• Linguist Joseph Grimes muses that asking "Is zero an even number?" to married couples is a good way to get them to disagree.
• Social theorist Anthony Wilden proposes that all rules have exceptions, giving an example: "Whole numbers are either odd or even, but zero is neither one nor the other."
• Columnist Tony Snow once wrote, "Question: Name one thing beneath Bill Clinton's dignity. Answer: This is a trick question, like asking whether zero is odd or even. It has no known answer." The attack on Clinton was to be expected; three readers who protested the comparison were more concerned with the mathematical error.
• Around the turn of the third millennium, media outlets noted a pair of unusual milestones: "11/19/1999" was the last calendar date composed of all odd digits that would occur for a very long time, and that "02/02/2000" was the first all-even date to occur in a very long time. Since these results make use of 0 being even, some readers disagreed with the idea.

There are also situations where calling zero even, or not, has consequences:

One third-party study guide for the GMAT states that 0 is not even, but the test's authors publish an official study guide that explicitly includes 0 in the even numbers. The correct answers to some of the GMAT's "data sufficiency" questions require that the usual rules for even numbers, such as n being even if (n + 2) is even, hold without exception for 0. The GRE also stipulates that 0 is even. Generally, on standardized tests, if a question asks about the behavior of even numbers, it might be necessary to keep in mind that zero is even.

The nominal evenness of zero is relevant to odd-even rationing systems. Cars might be allowed to drive or to purchase gasoline on alternate days, according to the parity of the last digit in their license plates. Half of the numbers in a given range end in 0, 2, 4, 6, 8 and the other half in 1, 3, 5, 7, 9, so it makes sense to include 0 with the other even numbers. The relevant legislation sometimes stipulates that zero is even to avoid confusion. "Penn State mathematician George Andrews, who recalls a time of gas rationing in Australia ... Then someone in the New South Wales parliament asserted this meant plates ending in zero could never get gas, because 'zero is neither odd nor even. So the New South Wales parliament ruled that for purposes of gas rationing, zero is an even number!'" In a modern news article on gas rationing based on license plate parity, care is given to explain that zero is considered an even number. In another example, a 1980 Maryland law specifies, "(a) On even numbered calendar dates gasoline shall only be purchased by operators of vehicles bearing personalized registration plates containing no numbers and registration plates with the last digit ending in an even number. This shall not include ham radio operator plates. Zero is an even number; (b) On odd numbered calendar dates ..." In fact, an odd-even restriction on driving in 1977 Paris did lead to confusion when the rules were unclear. On an odd-only day, the police avoided fining drivers whose plates ended in 0, because they did not know whether 0 was even.

In other situations, it can make sense to separate 0 from the other even numbers. On U.S. Navy vessels, even-numbered compartments are found on the port side, but zero is reserved for compartments that intersect the centerline. That is, the numbers read ...6420135... from port to starboard.

In the game of roulette, the casino has an interest in making sure that less than half of the numbers are counted as even. Thus the number 0 does not count as even or odd; a bet placed on either even or odd does not win if the ball falls on "0" or "00". The exact result depends on local rules, but the overall effect is to give the house an edge on "even money" bets. Similarly, the parity of zero can affect payoffs in prop bets when the outcome depends on whether some randomized number is odd or even, and it turns out to be zero. One bookmaker offers a "cricket roulette" in which a batsman who is dismissed for a duck wins for the bank.

The game of "odds and evens" is also affected: if both players cast zero fingers, who wins? Generally zero is counted as even. In fact, playing this game has been suggested as a way of introducing children to the concept that 0 is divisible by 2.