| Popis: |
Let \(\mathbb {R}\) be the set of real numbers. Throughout this book, the extended set of real numbers is \(\bar {\mathbb {R}} = \mathbb {R}\cup \{-\infty , +\infty \}\) and the extended subset of real positive numbers is \(\bar {\mathbb {R}}_+ = \mathbb {R}\cup \{+\infty \}\). An interval in \(\bar {\mathbb {R}}\) is a subset \(J\subseteq \bar {\mathbb {R}}\) with the property that, for all x, y ∈ J and for all z with \(\min \{ x, y\} < z < \max \{ x, y\}\), it follows that z ∈ J. If \(a, b\in \bar {\mathbb {R}}, a < b\), then \(]a, b[ = \{ x\in \bar {\mathbb {R}}: a < x < b\}\) is the open interval and \([a, b] = \{ x\in \bar {\mathbb {R}}: a\leq x\leq b\}\) is the closed interval of extremities a and b. Obviously \(\mathbb {R} = ]-\infty , +\infty [\) and \(\bar {\mathbb {R}} = [-\infty , +\infty ]\). |
