3 ms·
You're trying to explain the difference between countable and uncountable infinities here. The distinction is irrelevant in the context of computers. > By con
by otabdeveloper4 5y ago
You're trying to explain the difference between countable and uncountable infinities here.
The distinction is irrelevant in the context of computers.
> By contrast, you won't be able to construct a type that encodes exactly the set of real numbers.
You don't need to encode exactly, just like you don't need to encode the integers "exactly".
All you need is a way to guarantee a finite number of significant digits in your real number approximation.
Floating point numbers give you that, problem solved.
- Tainnor 5y ago> Floating point numbers give you that, problem solved. No. For example, floating point addition is not necessarily associative. In that sense, floating point numbers aren't even a field and it's wrong to say that they can be used as a stand-in for real numbers. Floating-point numbers are incredibly useful and it is amazing that we can exactly analyze their error bounds, but it's wrong to treat them as if they were real numbers.