From: Michael Orlitzky <michael@orlitzky.com>
Date: Thu, 14 Feb 2019 20:33:39 +0000 (-0500)
Subject: Add the four types of standard real intervals.
X-Git-Url: https://gitweb.michael.orlitzky.com/?a=commitdiff_plain;h=ce11edfc0c1c7b1dcbbbc21512336f91ad006863;p=mjotex.git

Add the four types of standard real intervals.
---

diff --git a/examples.tex b/examples.tex
index 26db4b1..897396c 100644
--- a/examples.tex
+++ b/examples.tex
@@ -69,6 +69,15 @@
     \begin{equation*}
       \unionmany{k=1}{\infty}{A_{k}} = \intersectmany{k=1}{\infty}{B_{k}}
     \end{equation*}
+
+    Finally, we have the four standard types of intervals in $\Rn[1]$,
+    %
+    \begin{align*}
+      \intervaloo{a}{b} &= \setc{ x \in \Rn[1]}{ a < x < b },\\
+      \intervaloc{a}{b} &= \setc{ x \in \Rn[1]}{ a < x \le b },\\
+      \intervalco{a}{b} &= \setc{ x \in \Rn[1]}{ a \le x < b }, \text{ and }\\
+      \intervalcc{a}{b} &= \setc{ x \in \Rn[1]}{ a \le x \le b }.
+    \end{align*}
   \end{section}
 
   \begin{section}{Cone}
diff --git a/mjo-common.tex b/mjo-common.tex
index e599201..38e08b3 100644
--- a/mjo-common.tex
+++ b/mjo-common.tex
@@ -124,3 +124,11 @@
 \providecommand*{\cartprodmany}[3]{ \binopmany{\bigtimes}{#1}{#2}{#3} }
 \providecommand*{\directsummany}[3]{ \binopmany{\bigoplus}{#1}{#2}{#3} }
 \providecommand*{\unionmany}[3]{ \binopmany{\bigcup}{#1}{#2}{#3} }
+
+
+% The four standard (UNLESS YOU'RE FRENCH) types of intervals along
+% the real line.
+\providecommand*{\intervaloo}[2]{ \left({#1},{#2}\right) } % open-open
+\providecommand*{\intervaloc}[2]{ \left({#1},{#2}\right] } % open-closed
+\providecommand*{\intervalco}[2]{ \left[{#1},{#2}\right) } % closed-open
+\providecommand*{\intervalcc}[2]{ \left[{#1},{#2}\right] } % closed-closed