I am writing a tech document and I would like to formulate "significantly" close/far. For example a certain suboptimal solution $x^{\dagger}$ is "significantly close" to the optimal solution $x^{*}$.
I was tempted to write something like $x^{*} - x^{\dagger} \simeq 0 $ however this is not correct because the "closeness" is relative to the problem and its parameters. In other words the difference might be 0.01, 0.1, 1, 5, 10 and still it would be considered to be "significantly close".
Thank you