What's it called when you treat intervals as numbers? Often in physics you have to do maths with a finite amount of digits, e.g. $\pi = 3.14$, but this is not exact and without knowing the next digit this is only correct in the interval $[3.135,3.145]$. But does this mean that you can treat $\pi$ as an interval instead of a number, and say $\pi = [3.135,3.145]$? Could this be generalised for a new type of "numbers" as intervals?
Something like:
$$
\vdots\\[0.5em]
-2 =\,[-3,-2]\\
-1 =\,[-2,-1]\\
-0 =\,[-1,-0]\\
0 =\,[0,1]\\
1 =\,[1,2]\\[0.5em]
\vdots
$$
where $a+b = [a_1,a_2]+[b_1,b_2] = [a_1+b_1,a_2+b_2]$
I'm sure must be some name for this concept, and I'd like to read more about it.

There is a branch of numerics that uses intervals instead of numbers, see: here
Interesting is the connection to automated proofs.
If the software would be error-free the computed intervals could be interpreted as proven bounds. I think they market this as reliable computing now.
