Arbitrary precision doesn't help with irrational numbers. You may be thinking of the "just use enough bits so you're sure the accumulated error isn't significa

Arbitrary precision doesn't help with irrational numbers. You may be thinking of the "just use enough bits so you're sure the accumulated error isn't significant" approach, which is essentially what modern floating-point attempts to do. There are still some pitfalls though, around doing an analysis that proves the bounds of said error in a given algorithm and data set. You might be interested in the concepts used in interval arithmetic [1] and specifically the work of Gustafson in designing some models for using those in scientific computing hardware. [1] https://en.wikipedia.org/wiki/Interval_arithmetic https://en.wikipedia.org/wiki/Interval_arithmetic