The book was speaking about approximations. Given a number and its approximant the error is (because you need to know which one is larger which is same thing as using absolute). But in real life we usally do not know how exactly close an approximant is. Because if we did then we would know what actual value of is, (which we do not know and thus we approximate).Originally Posted by OReilly
However, when we want to determine how close something is to something else, we use an inequality (which is possible in real life). And the inequality says how close something is, for example is the approximant is 4 decimal places corret which is accurate.