 That is, for any degree of approximation to the limit that we want, there is some degree of approximation for the input that suffices to guarantee that the function is that close. In the initial definition of a limit as \(x\) goes to \(+\infty\), we required \(x\) to ‘approximate’ \(+\infty\) by being sufficiently large, but now we require it to approximate \(a\) by having a difference from \(a\) that is sufficiently small, just as the values of the sequence or function approximate the limit \(l\).