 This fact about bounded, increasing sequences also underlies the use of infinite decimal notation for real numbers. When we say that the number \(\pi=3.1415926\dots\), we just mean that \(\pi\) is the limit of the sequence \(3, 3.1, 3.14, 3.141, \dots\). One fact about this notation that many people find surprising is that the decimal notation \(0.99999\dots\) is the limit of the sequence \(.9, .99, .999, \dots\), and thus is precisely 1. Some people feel the intuition that \(0.9999\dots\) should somehow denote a number ‘infinitely close’ to 1, but not equal to it. We will be able to make sense of an idea like this in section  3.4,  but it turns out that decimal notation is not the way to do it. For a useful demonstration of this point, see Vi Hart’s video   9.999... reasons that .999... = 1.