Is zero an even number?

http://www.bbc.co.uk/news/magazine-20559052

by ColinWright • 14 years ago

40 45 14 years ago

bbc.co.uk

huhtenberg• 14 years ago

> The use of the phrase "even number, or the number zero" implies that zero is not even.

Ah, no. It implies that some gas station attendants might think that it's not. It's idiot-proofing the instructions.

lazerwalker• 14 years ago

If that's the case, one could argue that "even number, including the number zero" would be an equally idiot proof but more technically accurate phrasing.

StavrosK• 14 years ago

Indeed it would. However, Bloomberg wasn't making a mathematical proclamation, he was telling people when they could get gas after their house was demolished. This isn't even an issue.

dkarl• 14 years ago

If that's the case, one could argue that "even number, including the number zero"

Then the hypothetical gas station attendant would argue that the instructions were self-contradictory and he was just doing his best to enforce them. It isn't just idiot-proofing, it's argument-proofing, making sure some self-important nit-picker doesn't disingenuously try to throw everything into chaos to prove that authority is stupid.

Heliosmaster• 14 years ago

One then might argue that the "or" is not exclusive in this context... but let's not be that geeky.

nodata• 14 years ago

Doesn't it depend if an idiot wrote the instructions to start with?

brightsize• 14 years ago

I don't live in Oregon or New Jersey. What's a gas station attendant?

eclipticplane• 14 years ago

New Jersey does not allow motorists to fill their own tanks using self-service pumps. It's a hold-over from the 40s, when gas pumps and gas tanks did not have all the safety features they have now, like automatic shut off valves and coatings to protect against static and sparks.

On the down side, it makes gas slightly more expensive. On the plus side, gas stations generally move quite quickly in New Jersey. You can go inside to buy a drink while the attendant fills your car, for example.

rmc• 14 years ago

Exactly. If they don't do this there will be arguments and disputes and within 24 hours they'd have to release a clarification to state the even/odd status of zero.

Leszek• 14 years ago

Slow news day over at the bbc?

dvanduzer• 14 years ago

It's often mentioned in media savvy circles that a necessary (though not sufficient) condition for something to be newsworthy is that it doesn't happen very often.

Widespread discussion of fundamental mathematical truths in popular culture seems rare enough to count as news.

JonnieCache• 14 years ago

This is from their magazine section, the equivalent to the glossy bit you get with a quality newspaper on the weekend.

bcuccioli• 14 years ago

The irony of this article is that the author is trying to sneer at someone for making a mathematical mistake, which is not technically wrong, but himself falsely asserts that "The use of the phrase 'even number, or the number zero' implies that zero is not even", which is not true in the usual first order logic.

zem5• 14 years ago

but "or" in english is not identical to "or" in first order logic. they're different domains that just happen to use the same symbol.

anonymfus• 14 years ago

Yes. In English "even number, or the number zero" technically can also mean that terms "even number" and "zero" have same meanings, i. e. "even number aka the number zero".

tsotha• 14 years ago

>...but himself falsely asserts that "The use of the phrase 'even number, or the number zero' implies that zero is not even", which is not true in the usual first order logic.

But in English it really does imply zero is not even. As a percentage of the population, just how many mathematicians do you think there are?

anonymouz2• 14 years ago

Without further clarifications it is at best ambiguous in English: Sometimes the "or" is meant to allow both options, sometimes not.

When mathematicians talk in English they usually (by convention) mean the "or" of first order logic (i.e., inclusive or). Since they happen to be the ones talking about even/odd numbers and they are a group of people that do require a language specific enough to have to specify whether the "or" is inclusive or exclusive, it seems like a good idea that such a statement should be taken in this framework.

shmageggy• 14 years ago

but himself falsely asserts that...

The author is female.

zem5• 14 years ago

key sentence:

> 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.

joejohnson• 14 years ago

Yes, it is. Please don't upvote fluff pieces like this.

zem5• 14 years ago

did you read the article or just the title?

> 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.

morsch• 14 years ago

That's interesting, but hardly unexpected from a cognitive perspective. Zero is even, but it's not a prototypical even number (like 2). Similarly, if you ask people whether an ostrich a bird, they take longer to respond than with a more typical example. A very clearly (and simply?) defined category such as even numbers is an interesting edge case of the phenomenon.

jonsen• 14 years ago

Is zero even a number?

jerryr• 14 years ago

I enjoyed these books on the history of that question:

Charles Seife's "Zero: The Biography of a Dangerous Idea" (http://www.amazon.com/Zero-Biography-Dangerous-Idea-ebook/dp...)

Robert Kaplan's "The Nothing That Is: A Natural History of Zero" (http://www.amazon.com/Nothing-that-Natural-History-ebook/dp/...)

Someone• 14 years ago

The book I recommend for this is "From One to Zero". http://www.amazon.com/From-One-Zero-Georges-Ifrah/dp/0670373.... The reviews on Amazon do not make me reconsider that. "From One to Zero" comes over as both having more content per page and more pages.

infinity• 14 years ago

That depends on which concept of "number" and which foundation you would accept as a basis for doing arithmetic.

I would expect any useful system of arithmetic, offering addition and subtraction, to contain some concept of "nothing". Because if a is something that might be subtracted from anything else including itself, we have the result that a - a is something we should be able to talk about, namely nothing.

If you accept a sufficiently strong set theory as a foundation of mathematics, for example the Zermelo Fraenkel set theory including the axiom of choice (ZFC), it is possible to use the finite ordinal numbers - which are actually sets - as the natural numbers.

From the ZFC axioms we have the existence of the empty set, often denoted by a pair of empty brackets {}.

We can then define numbers by using the empty set:

0 := {}

1 := {0} = {{}}

2 := {0,1} = {{},{{}}}

... and so on. By this definition zero is a number.

On the other hand, by defining numbers on the basis of set theory we seem to accept that numbers are sets. Some people will have very different opinions about this matter.

anonymouz2• 14 years ago

In fact, the Peano axioms are enough to represent the natural numbers, and they are much less general than ZFC. The construction with finite ordinals in ZF(C) constructs a model for it within ZF(C).

If you prefer something else than set theory, you should still be able to construct natural numbers satisfying the Peano axioms. In other words, any reasonable axiomatization of mathematics will give you the naturals.

agentq• 14 years ago

I tried to convince the croupier that zero was an even number, but alas ...

pandaman• 14 years ago

The policy is somewhat interesting as there are more odd days than even (if a month has 29 or 31 days then there will be two odd days in a row at the end of the month) yet it also allows more plates on the odd days (odd numbers + all other characters). If the last character on the NY plates is evenly distributed then there will be disproportionally more vehicles filling up on the odd days and it would be better to drive an even-numbered vehicle.

mikeash2• 14 years ago

That will really only matter if the policy remains in effect over a period of months, which it hasn't.

droithomme• 14 years ago

The reason the mayor said "an even number or zero" is because if he said "an even number", it's really obvious that many people with zero ending license plates would show up both days claiming zero was neither even nor odd, thinking they had found a loophole and/or that zero plate holders were lucky and special.

Explicitly including zero in the rule is not an assertion zero is not even, it is an attempt to head off the confusion, controversy, lawsuits, fights, and wasted time needed to later modify the rule when the inevitable controversy arises.

PuercoPop2• 14 years ago

You could say an even number, which includes zero for that effect.

PuercoPop2• 14 years ago

Why the downvoting? I was just pointing that the OC makes a non argument. If one wants to prevent ambiguity of the text, and one thinks that the evenness of is not clear for the intended audience, one adds a appositive parenthesis reinforcing that fact.

baddox• 14 years ago

I suspect the mayor's goal was to eliminate driver confusion, not to prevent this article from being written.

mikeash2• 14 years ago

And all of those potential confusion, controversy, lawsuits, fights, and wasted time come out of the fact that a lot of people don't think zero is even, which is the whole point they were trying to make.

omni• 14 years ago

Or that people are capable of being intellectually dishonest when it suits them.

anigbrowl• 14 years ago

Bullshit. Most of those people don't give a fuck whether zero is odd or even, they just want to buck the system. It's like those anti-tax nuts who claim their social security # doesn't belong to them, but to some 'straw man' identity, because the name on the social security card is in all caps.

Raphael• 14 years ago

> numbers to the power of two which would include two, four, six, eight or two, four, eight, 16

Ah, yes. Who could ever forget "2 ^ 2.5850"?

gjm11• 14 years ago

Two unrelated thoughts:

1. In the mayor's place, I'd have considered spelling it out explicitly: "drivers whose licence plates end in 0, 2, 4, 6, or 8 will be able to buy gas or diesel only on even-numbered days of the month", etc. This is both idiot-proof and pedant-proof.

2. I believe the Pythagoreans (ancient Greek, 6th century BCE) regarded both 0 and 1 as not being numbers, and as neither odd nor even.

Is zero an even number?

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