> you will only be able to get a solution of the form 2 ± ϵ for some arbitrarily small ϵ The problem with that from a UX perspective is that you won't even get

> you will only be able to get a solution of the form 2 ± ϵ for some arbitrarily small ϵ The problem with that from a UX perspective is that you won't even get to write out the first digit of the solution because you can never decide whether it should be 1.999...999something (which truncates to 1.99) or 2.000...000something (which truncates to 2.00). This is a well-known peculiarity of "exact" real computation and is basically one especially relevant case of the 'Table-maker's dilemma' https://en.wikipedia.org/wiki/Rounding#Table-maker%27s_dilemma https://en.wikipedia.org/wiki/Rounding#Table-maker%27s_dilem...