Nats start at 0, end of discussion - it's only logical to index by the naturals.
A dichotomy between "ℤ+" on the one hand versus "ℕ" on the other is just plain more convenient than a dichotomy between "ℤ+" and "ℕ" on the one hand versus "ℤ\ℤ-" on the other.
I prefer to start by zero; I think it is more useful in general, and makes more sense mathematically for many (although not all) purposes, and systems that you will find objects and operations that have these properties too.
Now you'll just bring out the people who start the naturals at 1.
It all makes perfect sense in the context of measuring.
Maybe a null terminated string could have length 0 if you don't count the terminator. But that 0 is a property of the "string" abstraction. The actual "array" would still be length 1.
Nope. The moment you "start" somewhere you occupy 1 unit of memory. Thus no longer an "array of length 0".
There is no such thing as an array of length 0. It absolutely does not exist. You cannot write source code to represent it.
ie assuming we are talking about the pure data structure of an array. Some languages may have some abstraction built on of arrays (ie c-strings) that can have length 0 but these are not "arrays" and if they are defined they still occupy 1 unit of memory for the terminator.
https://play.rust-lang.org/?version=stable&mode=debug&editio...
it's an array of length 0, but it can't be "used" because it has a length of 0 so it occupies no RAM
But such an array does not "start" at 0 as it does not exist. You need an array of at least length-1 to "start" at 0.
`for(int i=0; i < 0; ++i)` and it will run 0 times, the exact amount of times I expected
This loop is not processing any physically existing array. In fact the compiler would remove this block of code as it is a no-op.
iopq points out Rust as a language that does allow zero length arrays in a sibling comment.
While ISO C does not allow zero length arrays, GNU C does. There’s also flexible array members, which can be length 0.
Sure a language can define some abstraction that says "hey I'm length-0 array!". But this is more like a statement of "hey I don't exist yet, but if i do exist in the future I'll be of type array and at least length-1".
You can't access index 0 of a length-0 array.
You can only access index 0 of length-1+ array.
To take your ruler example and apply array logic to to. Say you are measuring a 2cm thing. If the ruler follows the index then it would show 1cm (the last index), and so you would have to add + to get the size/length.
Having the index not align with the size is a pain that results in a lot of +/-1 code that a compiler could just as easily have handled.
I'm not saying it has to be this way and it can't start with 1, I'm saying what you are pointing out as a flaw is actually the mixing of systems.
in computer programming teams it's best to adopt a standard unambiguous language to communicate to one another so as not have to constantly say "do you mean...?"
0..4
the second int occupies bytes
4..8
you can see the array up to the second int occupies the contiguous space 0..8 which 0..4*2 and it has TWO elements
Well, no, obviously you want to index by ordinals, and they start at "first".
Why not? "Every cardinality, except of the empty set, is a natural number" isn't very convincing to me, if we're making cardinal-based arguments.
Dijkstra's argument (https://www.cs.utexas.edu/users/EWD/ewd08xx/EWD831.PDF) is that we count the number of predecessors. This fits well with the mathematical usage, at least among mathematicians who care to dig into the order-theoretic foundations: the von Neumann construction of ordinals (and of cardinals as least ordinals of a fixed, well, cardinality), each finite ordinal is equal to its cardinality: 0 = \emptyset is a set with 0 elements, 1 = {0} is a set with 1 element, 2 = {0, 1} is a set with 2 elements, etc.
If you allow 0 as a valid ordinal, it unifies ordination and measure. That's the best reason to do so.
There. Djikstra as haiku.
Just to be clear, I wasn't making some sort of bizarre appeal to authority; whether something makes sense is a matter of taste, not of mathematics, and can't be proven or dis-. I meant only to respond to:
> In maths they always talk about the first element in a vector, not the zeroth. It is a bad argument to point to mathematics for using zero based indices.
I don't know for sure which convention is more common, though I suspect you're right that it's the 1-based convention, but I do know that it's false that 'they'—meaning, among others, we!—always talk about the first element/component in a vector. I probably will do that in a first Linear Algebra class, because the textbook often does and I don't want to introduce unnecessary confusion; but usually in my own work, and sometimes when I teach upper-level math classes, I use 0-based indexing when it's necessary to choose.
I think an age-based way to phrase it: in your 1st year, your age is 0; in your 2nd year, your age is 1; and so on. We can assign people numbers indicating what year of their lives they're in, or how many years they have lived, and both are fine, but we've settled on the latter.
That's not an argument. It's a coincidence. There are applications where what you care about is the number of predecessors (indeed, that's what the compiler cares about, which is why we have 0-indexing in the first place), but they are a tiny minority of all indexing.
> I think an age-based way to phrase it: in your 1st year, your age is 0; in your 2nd year, your age is 1; and so on.
But that isn't even true. No one ever reports the age of their new child as 0; instead, they will report a positive number of months, or -- if it's an extremely new child -- of weeks or days.
I think there's nothing to say to the first two sentences but that I regard it as an argument that may be more or less convincing. I don't know exactly what it means for something to be an argument vs. a coincidence; it is a coincidence that, say, my name is what it is, but it is nonetheless correct for me to argue that that is my name.
These are all conventions anyway, and there is not much use (or even meaning) in arguing about which one is the right or wrong convention, just which one makes more or less sense; and this is one way to make sense of 0-based indexing, though of course there are also ways to make sense of 1-based indexing.
I'm not sure I buy that these cases are a tiny minority, but I'm certainly in no position to produce any data to the contrary.
> > I think an age-based way to phrase it: in your 1st year, your age is 0; in your 2nd year, your age is 1; and so on.
> But that isn't even true. No one ever reports the age of their new child as 0; instead, they will report a positive number of months, or -- if it's an extremely new child -- of weeks or days.
I can believe that ages aren't reported that way, although I think that a child who will be 1 year in 1 year should logically be said to be 0 years; but we can avoid that debate by considering future years: in, to pick the example that applies to me, my 42nd year of life, I am 41 (I could say 41 and 1 month, but I don't—in fact, there's a Seinfeld joke about that). Similarly, the 42nd entry in a 0-indexed array is indexed 41. It doesn't have to be that way, but I don't think one can argue that there's anything logically amiss about it (nor about 1-based indexing … but we do have to pick one).
Sure. But we're talking about whether to index arrays from 0 or 1. It is true that naming an array element after the quantity of its predecessors will tell you the number of predecessors the element has. But that's not an argument for why you should do it; there would need to be some kind of benefit to having that information. Without a benefit, it's just something that happens to be true.
That's the difference between an argument and a coincidence.
the positive integers (whole numbers) 1, 2, 3, etc., and sometimes zero as well.