I’ve talked too much with mathematicians

You are talking to one right now :) (not sure if a bachelors degree is enough to call yourself one)

you can’t have 0 apples

You can actually. In fact, right at this moment I have 0 apples. If 0 is not natural, then you have no way of describing the number of apples I have.

There are a lot of concepts (degree of a polynomial, dimension of a space, cardinality of a set, in a graph) where 0 is a natural possibility.

So I think 1 indexing is fine, I use it all the time, but to me 0 belongs with the natutals. I will say tho, that 0 does not make sense to me as an ordinal. “He finished the race in 0-th place”???

I guess it depends on the place. But the arguments for not including seem futile, when

• we use 0 to even write the other natural numbers
• we define almost all of our algebraic objects (groups, rings/fields, modules/vector spaces, algebras) to include 0
• we don’t do modular arithmetic with {1,…,n} that would be crazy

Of course 0 vs no 0 only matters if you actually do arithmetic with it. If you only index you could just as well start with 5.

(The only reasons I can think of to start at 1 is that 1 is the 1-st element then and the sequence (1/n) is defined for all natural n)

Idk if you are trolling, but in most cases 0 is considered a part of the natural numbers. And there is a huge difference between the naturals and the integers: the naturals are for induction, the integers are for algebra.

Very good points! I only asked for features of the language itself, not for how specific libraries work or even more special stuff.

I don’t know about Japanese, but I did study rust (the programming language) with chatgpt and its really good for that, because you can keep asking questions and drilling down until you understand. (a human teacher might get tired) Only real problem I had was it kept forgetting the context. I didn’t really have problems with hallucination and even if i did I could just try the code, which will not work for Japanese.