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tanszek:oktatas:techcomm:mathematical_expressions_in_tex_language [2025/09/04 12:22] – [3. Basic Text Formatting in LaTeX] kissatanszek:oktatas:techcomm:mathematical_expressions_in_tex_language [2026/09/02 09:14] (current) – [7. Exercise] kissa
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 **Getting Started:** **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:** **Basic Document Structure:**
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 Use the ''\textbf{...}'' command:   Use the ''\textbf{...}'' command:  
-- Example: `\textbf{This is bold}` → **This is bold**+  - Example: ''\textbf{This is bold}'' → **This is bold**
  
 **Italic text** **Italic text**
  
 Use the ''\textit{...}'' command:   Use the ''\textit{...}'' command:  
-- Example: `\textit{This is italic}` → //This is italic//+  - Example: ''\textit{This is italic}'' → //This is italic//
  
 **Underline text** **Underline text**
  
 Use the ''\underline{...}'' command:   Use the ''\underline{...}'' command:  
-- Example: ''\underline{This is underlined}'' → __This is underlined__+  - Example: ''\underline{This is underlined}'' → __This is underlined__
  
 **Combining formats** **Combining formats**
  
 You can even combine them:   You can even combine them:  
-- Example: ''\textbf{\textit{Bold and italic}}'' → **_Bold and italic_** +  - Example: ''\textbf{\textit{Bold and italic}}'' → **//Bold and italic//** 
- +  - Example:
-== Example ==+
  
 <code LaTeX> <code LaTeX>
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 **Explanation:** **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:** **Tips:**
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 To refer to this equation later, use ''Equation \ref{eq:quadratic}''. 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}}
  
-==== 6. 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! 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}}
  
  
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 <code> <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: Squaring both sides:
-HERE COMES AN EQUATION.+EQUATION
  
 Multiplying both sides by b2: 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. 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: Dividing by 2:
-HERE COMES AN EQUATION.+EQUATION
  
 This implies that b2 is even, so b must also be even. 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> </code>
  
tanszek/oktatas/techcomm/mathematical_expressions_in_tex_language.1756988555.txt.gz · Last modified: by kissa