For example, \((\mathbb{Z}, d)\) is quasi-isometric to \((\mathbb{R}, d)\) where \(d(x, y) = |y - x|\), because the inclusion map \(\iota\) from \(\mathbb{Z}\) to \(\mathbb{R}\), \(\iota(n) = n\), is an isometry hence a quasi-isometry with \(L = 1\) and \(K = 0\), and each point in \(\mathbb{R}\) is no further than \(1/2\) away from an integer (in \(\mathbb{R}\)). Also, it is easy to see that for any real number \(x\), if \(g(x) =\) the nearest integer to \(x\) (or the greatest integer less than \(x\) if it is midway between integers) then \(g\) is a quasi-isometry from \(\mathbb{R}\) to \(\mathbb{Z}\) with \(L = 1\) and \(K =\frac{1}{2}\);.