Will resolve to YES if >50% at close, NO if <50% at close, and N/A if 50%.
Pros of 0 being a natural number:
Computers count from 0
Modular arithmetic and remainders include 0 as the first value (this is actually probably equivalent to the first point, now that i think about it)
The definition of the natural numbers (where n is defined as the size of the set containing the all the previously defined numbers) using sets relies on 0 being the first natural number
Pros of 0 not being a natural number:
0 has a lot of weird properties not shared by other very definitively natural numbers, which makes it awkward to include (ex. when defining things like 1/n where n is a "natural number")
0 is functionally symmetrical to ∞, which is definitely not a natural number
If anyone else brings up a good point about 0 being in or out of the set of natural numbers, I'll add it.
1,000Natural numbers are 1, 2, 3,…
Whole numbers include 0
Integers include the negatives of each natural number
Rational numbers include all fractions of integers as long as 0 is not in the denominator
Reals include irrational numbers
Complex include all a+bi where a and b are real and I is square root of -1
That is what we all learned in elementary school in US
Then in college, we developed more analytic definitions.
@PGeyer whole numbers and integers are the same thing. natural numbers include 0. without the 0, they aren't even a monoid.
@TonioKettner What I stated is what I learned both K-12 and in university, with two math degrees. It is a matter of convention. I am just sharing mine. You, yours. Evidence showing one must define your terms and not simply assume they are agreed upon. Even Wikipedia is lame on “natural number” definition, starting out with 1 2 3, then saying and maybe 0. https://en.wikipedia.org/wiki/Natural_number?wprov=sfti1#
In my convention, each term is a proper subset of the previous one, with no redundancy. Yours works for you. I believe the point of this question is that the word must always be defined in the text, which you and I can agree, is an inefficiency. Blame our different books and teachers, right? Until that, for me, whole numbers are monoid under both multiplication and addition. Natural are only monoid under multiplication.
It's a question of definition so it makes sense to look up the consensus, rather than coming up with our own definition: https://en.wikipedia.org/wiki/Peano_axioms define natural numbers to include 0.
@OlegEterevsky Defining the natural numbers in terms of the Peano axioms necessarily implies that before year 1889 there were no natural numbers.
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@Mira That is absolutely not true. That’s like saying you could fly before newton discovered gravity
@JohnKelly but isn't whether math was "invented" or "discovered" a whole different debate? like, if newton had instead invented gravity, then hell yeah everyone would've been superman prior to gravity
@michelangelo Natural numbers are a subset of the integers. This is like saying, "2 is an integer, not an even number."
@michelangelo And the question here is a matter of convention, not a mathematical fact. There's no way to resolve it, except for everyone to decide to follow the same convention, which they don't.
@michelangelo Many people use a different definition of natural number. It's flatly false to say they "are positive integers" as though that's the unique universal definition of the term, because it's not. For example, the ISO 80000-2 standard includes 0.
@michelangelo You are just paraphrasing the actual question, and saying it is false.
Just stating 0 is not a natural number isn’t an arguments, the arguments should be about why we would want it included or not in the natural numbers.
And that most people (or mathematicians) would not include it, would be a good argument, if you are able to show it is true.
There are a lot of other good arguments for or against, but just stating it isn’t included, isn’t one.
@dionisos As I already stated: "0 is not a positive integer. Natural numbers are positive integers."
@michelangelo The fact we have a simple term for "positive integers", go against the idea to use "natural numbers" as a synonym (if we doesn’t have a similar simple term for natural numbers⋃{0}).
@dionisos "non-negative integers"
(myself, I only ever say "natural numbers" when it doesn't matter whether we start from 0 or from 1, and always say either "non-negative integers" or "positive integers" whenever it does)
@ArmandodiMatteo I think "non-negative integers" is slightly less simple.
But indeed, it would be a weak argument against natural numbers not including 0, but it is at least not a strong argument against natural number including it.
I think other arguments given in the comment section are more important.
@dionisos "I think "non-negative integers" is slightly less simple."
If that's because it's one more syllable, that's language-dependent (IIRC the French for "non-negative" is "positif" and the French for "positive" is "strictement positif") and having e.g. "natural number" and "nombre naturel" mean different things just because of this would feel silly to me
@ArmandodiMatteo I agree it would be silly to have two different meanings in two different languages. It already bad that "positive numbers", doesn’t mean the same thing in all languages, and we don’t need more stuffs like that.