Is zero an even number? | Hacker News Reader

Is zero an even number?

bbc.co.uk

40 pointsColinWright45 comments

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.

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

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.

It looks like you meant "'an even number, which includes zero' for that effect", but on first reading, it appeared to me (and perhaps your downvoters), that you meant "'an even number', which includes zero for that effect", which would be a significantly less productive comment.

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

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.

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

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.

> 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.

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.

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.

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.

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

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

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

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.

> On the plus side, gas stations generally move quite quickly in New Jersey.

This is really not the case at a busy station. You have to wait for the attendant to come to you to start filling the tank and then you have to wait again after the tank is full. At most, they'll have two attendants for the entire station, which means you end up waiting while he's servicing the other customers.

On the subject of annoying service stations/gas stations/petrol stations, the tirade that greets payment is now insane in New Zealand. Do you have fly buys? AA card? Discount vouchers? Would you like any of these sweets that are on special? A car wash? I know that the staff are told to ask these questions, but if they can find a way to make the service more irritating, I'd be slightly impressed.

  On the down side, it makes gas slightly more expensive.

Oh? For many years a fill-up was substantially cheaper in New Jersey than neighboring states, and whenever I was driving up from Washington, DC area to New York or Boston I would try to fill it in New Jersey (a full tank of gas was not a trivial expense for a poor grad student). The difference is small these days.

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.

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.

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.

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".

which is clearly yet another, different use of "or". i don't know why people are quibbling about this point, the usage the article cites pretty unambiguously means "all the even numbers, and zero even if you don't consider it an even number"

>...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?

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.

but himself falsely asserts that...

The author is female.

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

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.

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

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.

Slow news day over at the bbc?

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.

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

Is zero even a number?

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/...)

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.

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.

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.

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.

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

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.

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.

yeah, not unexpected, but definitely interesting. certainly not a "fluff piece" as the grandparent was claiming.

> 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"?

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