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I'm not arguing that the natural numbers should start from one, rather that the usual path for developing the natural numbers starting with set theory is that z

I'm not arguing that the natural numbers should start from one, rather that the usual path for developing the natural numbers starting with set theory is that zero is the size of a set with nothing in it. 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. It is not at all common to use zero based indexing there.

JadeNB 4y ago
I'm a mathematician, and 0-based indexing makes way more sense to me. Dijkstra's argument (https://www.cs.utexas.edu/users/EWD/ewd08xx/EWD831.PDF 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.
- salty_biscuits 4y ago
  I'm a mathematician too, and it doesn't make sense to me. It seems somewhat arbitrary depending on the application, i.e. I think it is a type problem. We use an Int to mean something special about array elements. I'd be happier with first() and last() methods really, I don't care for coming up with meanings based on implementation details.
  - samatman 4y ago
    The question is whether 0 is a valid ordinal. If it is, why skip it? 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.
  - JadeNB 4y ago
    > I'm a mathematician too, and it doesn't make sense to me. 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.

JadeNB 4y ago

I'm a mathematician, and 0-based indexing makes way more sense to me. Dijkstra's argument (https://www.cs.utexas.edu/users/EWD/ewd08xx/EWD831.PDF 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.

salty_biscuits 4y ago
I'm a mathematician too, and it doesn't make sense to me. It seems somewhat arbitrary depending on the application, i.e. I think it is a type problem. We use an Int to mean something special about array elements. I'd be happier with first() and last() methods really, I don't care for coming up with meanings based on implementation details.
- samatman 4y ago
  The question is whether 0 is a valid ordinal. If it is, why skip it? 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.
- JadeNB 4y ago
  > I'm a mathematician too, and it doesn't make sense to me. 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.