For anyone wondering about the difference between endpoint-based interval arithmetic ([a,b]) and midpoint-radius ([m +/- r]) arithmetic (ball arithmetic): they are often interchangeable, but they have different tradeoffs. Roughly speaking, standard interval arithmetic is better for subdivision of space, while ball arithmetic is better for representing individual numbers.
A good technical introduction to ball arithmetic is this paper by Joris van der Hoeven: https://www.texmacs.org/joris/ball/ball.html