> IMO it's unfortunate that most languages default to floating-point. Most beginning programmers would be better served …
Most languages, most of the time, are not used by beginners.
Most languages, most of the time, are not used by beginners.
However, if you use "beginner" to the knowledge gained, it might not be. If you only ever make webpages, even if you have made 100s you could still be a novice programmer because you never branched out enough to learn new programming concepts.
If a programming language makes it easy to do something moderately, but it is hard to do it well. Programmers who only know that language are likely to have a gap in their stills. Floating point (in most languages) is easy to gets the basics working, but are hard to do well and very hard to do perfectly. This leads to a lot of programmers not learning floating point well.
In this specific case representing non-integer numbers effectively on a binary device is complex. If you use a different representation than IEEE floats you just give a different set of corner cases and unexpected outcomes.
Don't let a novice build software you need to be correct without supervision, and if you are a novice expect to make mistakes, just like if I were to build a website I wouldn't expect my style choices to render appropriately on a wide range of devices... that's complex too!
Except, of course, at lower levels of abstraction - where IEEE floats are what the hardware implements. Lower level languages use 8-, 16-, 32-bit integers, they use IEEE floats and doubles, and they make these choices for pretty solid reasons.
Higher level languages make different choices (arbitrary precision integers are common in interpreted languages, eg). Libraries support all kinds of options up and down the stack.
In what way are rationals not the same number set? In the strictest sense basically none of the proposed versions have the same number set, but in a broad sense, they all represent a useful subset of rationals, right?
Maybe I also missed something obvious, so I'd like to satisfy my curiosity!
I don't know that it's necessarily as significant a difference as I'd first considered it to be, though.
Also, I think I'm too tired by now, I get confused too much between the rationals as the rational numbers \mathbb{Q} and the rationals as an implementation of rational numbers using a quotient of two integers.
- An experienced programmer would know that IEEE FP hardware is ubiquitous. Why would a language eschew that hardware capability by default? If anything, I would assume that any unfamiliar general-purpose language DOES start from that point (using IEEE float to represent non-integer numbers) because of historical precedent.
- "Number" is about as vague as you can get for a type name. Maybe personal bias here, but I find that vagueness invites research up front. "Time to read the documentation."
(I still expect a language newbie to get various bugs in new Javascript code, because the footguns in that language differ from the footguns in something like C++.)