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Author SHA1 Message Date
23c5c26472 Artifacts opslaan
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2026-01-22 23:43:59 +01:00
b27c0d1872 Geen sudo meer nodig
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2026-01-22 23:41:42 +01:00
b92d0a5a97 Smerige sudo
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2026-01-22 23:35:56 +01:00
7fbca3031a Poging om jenkins uit het slop te trekken
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2026-01-22 23:33:21 +01:00
12ba818631 Fix on template
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2025-11-21 10:15:10 +01:00
bc10cf8736 https ipv ssh voor de buildserver
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2025-11-16 00:50:32 +01:00
83c9218b81 Vieze workspace
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2025-11-16 00:45:26 +01:00
a7ec28cf5c Overbodig build script nu
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2025-11-16 00:37:06 +01:00
9ea1970fcf Fixed submodule 2025-11-16 00:36:47 +01:00
adcf470b30 Fix voor template, hopelijk nu werkend op buildsetup
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2025-11-16 00:31:46 +01:00
108ef1755a Revert "Poging met een dockerfile"
This reverts commit d2b0965281.
2025-11-15 20:59:52 +01:00
d2b0965281 Poging met een dockerfile
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2025-11-15 20:37:43 +01:00
ad278c6e66 Libertinus installeren met tlmgr
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2025-11-15 20:32:03 +01:00
40e3f57f5e Poging om font werkend te krijgen
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2025-11-15 20:16:50 +01:00
1bb9abb8cf Poging tot herstructurering om latexmk beter te benutten
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2025-11-15 20:02:47 +01:00
b1d3f25d48 In goede map
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2025-11-15 15:16:28 +01:00
029f0fe6d6 Image goed gebruiken
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2025-11-15 15:10:50 +01:00
85bdd56b1c Met sudo proberen
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2025-11-15 15:07:10 +01:00
cdbf024243 Correcte manier van bash installeren
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2025-11-15 15:05:49 +01:00
4b69b4ed5d Met bash geinstalleerd
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2025-11-15 15:03:46 +01:00
2f080802fb File expliciet uitvoeren met bash?
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2025-11-15 14:02:35 +01:00
0bf782be40 Output van file tonen als debugging
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2025-11-15 14:01:34 +01:00
2665c4b0c1 Meer debugging
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2025-11-15 13:59:48 +01:00
13455b406d New container image
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2025-11-15 13:30:30 +01:00
81586f7f19 Testing in production, check of repo wel in docker container komt
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2025-03-04 11:17:07 +01:00
d371820b74 Docker als agent in jenkinsfile
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2025-02-23 22:39:47 +01:00
9e486162f7 Nieuwe Jenkins setup testen
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2025-02-23 22:27:36 +01:00
13069e68ea Merge branch 'master' of ssh://212.132.118.65:55556/flip/real_analysis
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2025-02-22 17:17:34 +01:00
559d27267c Huidige datum toegevoegd 2025-02-22 17:17:24 +01:00
3e210ca9ba Finished git submodule test
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2024-06-18 10:57:28 +02:00
603241fce5 Test git submodule on commit
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2024-06-18 10:55:23 +02:00
11 changed files with 18 additions and 121 deletions

2
.gitmodules vendored
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@@ -1,4 +1,4 @@
[submodule "latex-homework"]
path = assignments/template
path = src/template
url = https://github.com/gijs-pennings/latex-homework.git
branch = master

15
Jenkinsfile vendored
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@@ -1,10 +1,12 @@
pipeline {
agent {label 'linux'}
agent any
stages {
stage('Build') {
steps {
echo 'Starting build step...'
sh './scripts/build.sh'
sh 'latexmk -pdf -outdir=out main_text.tex'
archiveArtifacts artifacts: 'out/main_text.pdf'
}
}
@@ -13,8 +15,13 @@ pipeline {
stage('Deploy') {
steps{
echo 'Starting deploy step...'
sh 'cp assignments/main_text.pdf /var/www/zwietering.eu/pdfs/real_analysis.pdf'
sh 'cp out/main_text.pdf /var/www/zwietering.eu/pdfs/real_analysis.pdf'
}
}
}
}
post {
cleanup {
cleanWs()
}
}
}

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@@ -1,75 +0,0 @@
\documentclass[../main_text.tex]{subfiles}
\begin{document}
\setcounter{exercise}{0}
\part{Assignment 4}
\exercise*
\begin{tcolorbox}
We say a set $F \subset \R$ is \textit{closed} if its complement $F^c := \R \backslash F$ is open. Since
$\emptyset$ and $\R$ are open, it follows that $\emptyset$ and $\R$ are closed as well.
\begin{enumerate}[label=\emph{(\alph*)}]
\item Let $a,b \in \R$ with $a < b$. Prove that $[a,b]$ is closed.
\item Is the set $\Z \subset \R$ closed? Provide a proof to substantiate your claim.
\item Is the set of rationals $\Q \subset \R$ closed? Provide a proof to substantiate your claim.
\end{enumerate}
\end{tcolorbox}
\begin{enumerate}[label=\emph{(\alph*)}]
\item The complement of $[a,b]$ is equal to the union of $(-\infty, a)$ and $(b, \infty)$. So, we have to prove
that both these sets are open. But we have already done so in the assignment of the previous week, so I'll just
leave it at that.
\item To prove that $\Z \subset \R$ is closed, we have to prove that the complement is open. Since the complement
consists of the union of a countably infinite number of open intervals $(a, b)$ such that $a < b$, we know
from a combination of earlier exercises that this is the case. This is because any interval $(a, b)$ is open
if $a,b \in \R$ such that $a < b$ and for any two open interval $A$ and $B$ that are open, then $A \cup B$
is open as well.
\item I claim that the set of rationals isn't closed in $\R$. This is because there doesn't exist any interval
$(a,b)$ where $a,b \in \Q$ such that $a < b$, since for any $a$ and $b$ you can always find a $c$ such that
$a < c < b$. This makes it impossible to find an $\epsilon > 0$ such that for any $x \in (a,b)$,
$(x - \epsilon, x + \epsilon)$ is also in $(a,b)$ but in such a way that it only contains irrational numbers.
This argument makes use of the fact that $\Q$ is dense in $\R$.
\end{enumerate}
\exercise*
\begin{tcolorbox}
\begin{enumerate}[label=\emph{(\alph*)}]
\item Let $\Lambda$ be a set (not necessarily a subset of $\R$), and for each $\lambda \in \Lambda$, let
$F_\lambda \in \R$. Prove that if $F_\lambda$ is closed for all $\lambda \in \Lambda$ then the set
\begin{equation*}
\bigcap_{\lambda \in \Lambda} F_\lambda = \{x \in \R : x \in F_\lambda \text{ for all }
\lambda \in \Lambda\}
\end{equation*}
is closed.
\item Let $n \in \N$, and let $F_1,...,F_n \subset \R$. Prove that if $F_1,...,F_n$ are closed then the set
$\bigcup_{m=1}^n F_m$ is closed.
\end{enumerate}
\end{tcolorbox}
This exercise is very similar to an exercise of the previous assignment, in which we looked at unions and intersections
of \textit{open} intervals, whereas in this exercise, it's all about closed intervals. As the definition of closed
intervals is intricately linked to the definition of open intervals, the following arguments will look very similar and
shouldn't be surprising.
\begin{enumerate}[label=\emph{(\alph*)}]
\item Non-formally speaking, in this exercise we want to prove that any intersection of closed sets in $\R$, is
closed itself. In order to make this formal, we will assume that $F_\lambda$ is closed for all $\lambda \in
\Lambda$ and follow the definition as presented.
So, let us assume that $F_\lambda$ is closed for all $\lambda \in \Lambda$. Following the definition of closed
sets, this means that the complement of $F_\lambda$ is open. Let's call the complement $\R \backslash F_\lambda =
U_\lambda$. Similarly, proving $\bigcap_{\lambda \in \Lambda} F_\lambda$ is closed, means we need to prove its
complement is open. From De Morgan's laws, it follows that $\R \backslash \bigcap_{\lambda \in \Lambda}
F_\lambda = \bigcup_{\lambda \in \Lambda} U_\lambda$.
We already proved this statement in exercise 5.b of week 3.
\item Similarly to the previous exercise, non-formally speaking we want to prove that any union of closed sets in
$\R$ is closed itself. Again, we will assign the complement of $(F_n)^c = U_n$, since we can't directly prove
a set is closed; we can only use the definition of closedness by proving something on open sets.
In the same vein, in order to prove that $\bigcup_{m=1}^n F_m$ is closed, we can only try and prove that its
complement is open. Using De Morgan's laws, $(\bigcup_{m=1}^n F_m)^c = \bigcap_{m=1}^n U_m$. This is the same
exercise as exercise 5.c from week 3, which also already proves the theorem.
\end{enumerate}
\end{document}

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@@ -1,4 +1,4 @@
\documentclass{template/homework}
\documentclass{src/template/homework}
\usepackage{enumitem} % Gives access to better enumeration items
\usepackage{tcolorbox} % Gives boxes
@@ -6,17 +6,15 @@
\title{MIT OCW Real Analysis}
\author{Philippe H. Zwietering}
\date{}
\date{\today}
\begin{document}
\maketitle
\tableofcontents
\clearpage
\subfile{week1/main.tex}
\subfile{./src/week1.tex}
\clearpage
\subfile{week2/main.tex}
\subfile{./src/week2.tex}
\clearpage
\subfile{week3/main.tex}
\clearpage
\subfile{week4/main.tex}
\subfile{./src/week3.tex}
\end{document}

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@@ -1,33 +0,0 @@
#!/bin/bash
# Build all directories
subdirectory_file_name=main
cd assignments
for D in *; do
if [ "${D}" != "template" ] && [ -d "${D}" ]; then
echo "Building ${D}..."
cd "${D}"
pdflatex -interaction=batchmode -halt-on-error "${subdirectory_file_name}.tex"
pdflatex -interaction=batchmode -halt-on-error "${subdirectory_file_name}.tex"
cd ..
fi
done
# Build main PDF
main_file_name=main_text
echo "Building main PDF..."
pdflatex -interaction=batchmode -halt-on-error "${main_file_name}.tex"
pdflatex -interaction=batchmode -halt-on-error "${main_file_name}.tex"
# Clean up
rm -rf *.aux *.log *.out *.toc
for D in *; do
if [ "${D}" != "template" ] && [ -d "${D}" ]; then
cd "${D}"
rm -rf *.aux *.log *.out *.toc
cd ..
fi
done

1
src/template Submodule

Submodule src/template added at bb25980b30