201–210 of 702 posts
Edsger Dijkstra wrote an interesting article titled 'why numbering should start at 0'. Perhaps not answering the question directly but an interesting read nonetheless. https://www.cs.utexas.edu/users/EWD/transcriptions/EWD08xx/E...
Dijkstra's answer (linked in the article) is best: "When dealing with a sequence of length N, the elements of which we wish to distinguish by subscript, the next vexing question is what subscript value to assign to its starting element. Adhering to convention a) yields, when starting with subscript 1, the subscript range 1 ≤ i https://www.cs.utexas.edu/users/EWD/transcriptions/EWD08xx/E...
I don't understand why 0 ≤ i ≤ N wouldn't have worked instead, since you already have a less than or equal operator at 0.
Here's a discussion from some years ago that starts with some of Guido's thoughts on array indexing and moves on to the QuickDraw coordinate plane and points and rectangles, including how grid lines and points are infinitely thin/small, but pixels occupy the space between the grid lines.
Earlier quoted context omitted.
In that specific case I'd do the following: for (size_t i = n; i-- > 0 ;) ... Or count from `length` to 1, but subtract 1 in the loop body, or count up and subtract the length in the loop body. Any modern compiler should be able to optimise these to be equivalent. In the majority of cases, counting down is not necessarily. Nor is ordered iteration. Most languages have a `for each` style syntax that's preferable anywa…
Ah yes, the goes-to operator -->
Other advantages of zero based indexing, beyond being 'closer to the machine': It works better with the modulo operator: `array[i%length]` vs `array[(i+length-1)%length+1]`. Or you would have to define a modulo-like operator that maps ℕ to [1..n]. It works better if you have a multi-dimensional index, for example the pixels in an image. With 0 based indexing, pixel `(x,y)` is at `array[x+width y]`. With 1 based index…
Edsger Dijkstra wrote an interesting article titled 'why numbering should start at 0'. Perhaps not answering the question directly but an interesting read nonetheless. https://www.cs.utexas.edu/users/EWD/transcriptions/EWD08xx/E...
I've never understood the first half of Dijkstra's argument. Unless we are programming a theoretical Turing machine, there will also be a maximum number that can be represented, so the argument about using inclusive bounds for the lower end also applies to the the upper end. So you can't represent all numbers with a single range style. You either end up excluding the smallest number, the largest number, or the empty…
It really comes down to a choice between a machine-focused (0) or human-focused (1) approach. The 0 makes a lot of sense in a C pointer world where memcpy and other alike functions can be written very thight. The 1 makes a lot of sense in a human world, when we count, we start at 1, we talk about the "1st", counting on finger starts with 1, etc. I once were at a Lua (1 indexed language) conference where this was disc…
> The 1 makes a lot of sense in a human world, when we count, we start at 1 As a kid I learned "one one-thousand, two one-thousand, three one-thousand" when counting time out loud, but at some point I realized this was incorrect. The prefix is the start of the nth second but it isn't complete yet, so for example stopping in the middle of saying "two one-thousand" you actually haven't reached two seconds yet. My fix w…
Doesnt sound half bad
It really comes down to a choice between a machine-focused (0) or human-focused (1) approach. The 0 makes a lot of sense in a C pointer world where memcpy and other alike functions can be written very thight. The 1 makes a lot of sense in a human world, when we count, we start at 1, we talk about the "1st", counting on finger starts with 1, etc. I once were at a Lua (1 indexed language) conference where this was disc…
TBH humans would have been better of if we were 0-based, it's just a convention. And we have the confusing language where "20th century" means 1900's. If we wanted to bring the 1-indexing we use in language to the fullest extent here to fix that particular issue, time counting would have to start at 1111. Except that won't work once reaching 5-digit years.
If we would start with "zeroeth" instead of "1st", then this would have solved itself and 20th century would mean 20xx's.
It really comes down to a choice between a machine-focused (0) or human-focused (1) approach. The 0 makes a lot of sense in a C pointer world where memcpy and other alike functions can be written very thight. The 1 makes a lot of sense in a human world, when we count, we start at 1, we talk about the "1st", counting on finger starts with 1, etc. I once were at a Lua (1 indexed language) conference where this was disc…
It really comes down to a choice between a machine-focused (0) or human-focused (1) approach. The 0 makes a lot of sense in a C pointer world where memcpy and other alike functions can be written very thight. The 1 makes a lot of sense in a human world, when we count, we start at 1, we talk about the "1st", counting on finger starts with 1, etc. I once were at a Lua (1 indexed language) conference where this was disc…
TBH humans would have been better of if we were 0-based, it's just a convention. And we have the confusing language where "20th century" means 1900's. If we wanted to bring the 1-indexing we use in language to the fullest extent here to fix that particular issue, time counting would have to start at 1111. Except that won't work once reaching 5-digit years.
If we would start with "zeroeth" instead of "1st", then this would have solved itself and 20th century would mean 20xx's.
I especially don't understand why mathematicians use 1-based indexing (for matrix rows/columns etc...). Like programmers, they should see the advantages of starting at 0 (e.g. the coordinates of subdividing into block matrices are simpler if starting at 0). Mathematicians do start at 0 for the origin of plots, after all.