Category:Usual Ordering on Extended Real Numbers
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This category contains results about Usual Ordering on Extended Real Numbers.
Let $\overline \R$ denote the extended real numbers.
Extend the natural ordering $\le_\R$ on $\R$ to $\overline \R = \R \cup \set {+\infty, -\infty}$ by imposing:
- $\forall x \in \overline \R: -\infty \le x$
- $\forall x \in \overline \R: x \le +\infty$
That is, considering the relations $\le$ and $\le_\R$ as subsets of $\overline \R \times \overline \R$:
- ${\le} := {\le_\R} \cup \set {\tuple {x, +\infty}: x \in \overline \R} \cup \set {\tuple {-\infty, x}: x \in \overline \R}$
where $\tuple {x, +\infty}$ and $\tuple {-\infty, x}$ denote ordered pairs in $\overline \R \times \overline \R$.
The ordering $\le$ is called the (usual) ordering on $\overline \R$.
Pages in category "Usual Ordering on Extended Real Numbers"
The following 2 pages are in this category, out of 2 total.