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--- tanszek:oktatas:techcomm:mathematical_expressions_in_tex_language [2024/09/10 08:54] – [1. Introduction to LaTeX] kissa
+++ tanszek:oktatas:techcomm:mathematical_expressions_in_tex_language [2026/09/02 09:14] (current) – [7. Exercise] kissa
@@ Line 19: / Line 19: @@
 **Getting Started:**
-  - **Overleaf**: We will use Overleaf, a free online LaTeX editor, which allows you to write and compile LaTeX documents directly in your browser.
+  - **Papeeria**: We will use Papeeria, a browser-based LaTeX editor that runs document compilation in the cloud: [[https://www.papeeria.com/]]
-    - Sign up at [[https://www.overleaf.com/|Overleaf]].
-    - Overleaf offers collaborative features, version control, and a vast library of LaTeX templates.
 **Basic Document Structure:**
@@ Line 55: / Line 53: @@
 </code>
-This code will became:
+This code will become:
 {{:tanszek:oktatas:techcomm:pasted:20240902-141219.png}}
@@ Line 90: / Line 88: @@
 {{:tanszek:oktatas:techcomm:pasted:20240902-141644.png}}
-==== 3. Special Mathematical Symbols in LaTeX ====
+==== 3. Basic Text Formatting in LaTeX ====
+LaTeX also allows you to format text, which is useful for emphasizing certain parts of your documents.
+**Bold text**
+Use the ''\textbf{...}'' command:
+  - Example: ''\textbf{This is bold}'' → **This is bold**
+**Italic text**
+Use the ''\textit{...}'' command:
+  - Example: ''\textit{This is italic}'' → //This is italic//
+**Underline text**
+Use the ''\underline{...}'' command:
+  - Example: ''\underline{This is underlined}'' → __This is underlined__
+**Combining formats**
+You can even combine them:
+  - Example: ''\textbf{\textit{Bold and italic}}'' → **//Bold and italic//**
+  - Example:
+<code LaTeX>
+\documentclass{article}
+\begin{document}
+Here is some \textbf{bold text}, some \textit{italic text}, and some \underline{underlined text}.
+You can also combine them, like \textbf{\textit{bold and italic}}.
+\end{document}
+</code>
+This will become:
+{{:tanszek:oktatas:techcomm:pasted:20250904-122112.png}}
+==== 4. Special Mathematical Symbols in LaTeX ====
 LaTeX provides a variety of symbols to accurately represent mathematical expressions.
@@ Line 134: / Line 172: @@
 This represents the definite integral of $x \sin(x)$ with respect to $x$ from $a$ to $b$.
-==== 4. Aligning Equations ====
+==== 5. Aligning Equations ====
 === Align Environment ===
@@ Line 160: / Line 198: @@
 **Explanation:**
-  - **\usepackage{amsmath}**: The `amsmath` package is required for advanced mathematical typesetting features, including the `align` environment.
+  - **\usepackage{amsmath}**: The ''amsmath'' package is required for advanced mathematical typesetting features, including the ''align'' environment.
-  - **&**: This symbol is used to align equations at the specified point, usually before an operator like `=`.
+  - **&**: This symbol is used to align equations at the specified point, usually before an operator like ''=''.
 **Tips:**
@@ Line 175: / Line 213: @@
 To refer to this equation later, use ''Equation \ref{eq:quadratic}''.
+==== 6. Lists ====
+LaTeX provides environments for creating both unordered and ordered lists.
+=== Unordered Lists ===
+Use the ''itemize'' environment to create a bulleted list. Each item starts with the \item command.
+<code LaTeX>
+\begin{itemize}
+  \item apple
+  \item banana
+  \item raspberry
+\end{itemize}
+</code>
+{{:tanszek:oktatas:techcomm:pasted:20260902-085819.png}}
+=== Ordered Lists ===
+Use the ''enumerate'' environment to create a numbered list.
+<code LaTeX>
+\begin{enumerate}
+  \item Denver Broncos
+  \item Buffalo Bills
+  \item Dallas Cowboys
+\end{enumerate}
+</code>
+{{:tanszek:oktatas:techcomm:pasted:20260902-085831.png}}
-==== 5. Exercise ====
+==== 7. Exercise ====
 Reproduce the following mathematical proof in LaTeX. Use inline and display math, as well as basic and special symbols! Save the result in PDF format!
-{{:tanszek:oktatas:techcomm:pasted:20240902-144955.png}}
+{{:tanszek:oktatas:techcomm:pasted:20260902-091119.png}}
@@ Line 186: / Line 255: @@
 <code>
-Proof: √2 is Irrational
+Proof: 2 is Irrational
-Assume, for contradiction, that √2 is rational. Then it can be expressed as a fraction a/b, where a and b are coprime integers.
+Assumptions:
+Assume, for contradiction, that 2 is rational.
+It can therefore be expressed as a fraction a/b.
+a and b are coprime integers.
-Then:
+We can write:
-HERE COMES AN EQUATION.
+EQUATION
 Squaring both sides:
-HERE COMES AN EQUATION.
+EQUATION
 Multiplying both sides by b2:
-HERE COMES AN EQUATION.
+EQUATION
 This implies that a2 is even, so a must also be even. Let a = 2k for some integer k.
-Substituting into the equation:
+Substituting a = 2k into the equation:
-HERE COMES AN EQUATION.
+EQUATION
 Dividing by 2:
-HERE COMES AN EQUATION.
+EQUATION
 This implies that b2 is even, so b must also be even.
-But if both a and b are even, they are not coprime, which contradicts our original assumption. Therefore, √2 must be irrational.
+Conclusion: If both a and b are even, then they are not coprime.
+This contradicts our original assumption. Therefore, 2 is irrational.
 </code>