{% abstract %}
This project is called jekyll-latex. It features the beautiful
typography of <span class="latex">L<span>a</span>T<span>
e</span>X</span> and it includes MathJax so you can render
gorgeous equations like this one below:
$$ J(\theta) =\frac{1}{2m}
[\sum^m_{i=1}(h_\theta(x^{(i)}) -
y^{(i)})2 + \lambda\sum^n_{j=1}\theta^2_j $$
{% endabstract %}

Table of Contents

• Table of Contents
• Theorems, Definitions, and Proofs
• HTML Elements
  • Text Formatting
  • Definition Lists
  • Blockquotes
  • Tables
  • Images
  • Lists
    • Unordered List
    • Ordered List

# Table of Contents
* TOC
{:toc}

Theorems, Definitions, and Proofs

{% theorem %}

The real numbers $\mathbb{R}$ are uncountable

{% endtheorem %}



{% proof %}

If $\mathbb{R}$ is countable, then [0, 1] is countable as well. Hence
there exists a map C from $\mathbb{N}$ onto [0, 1] with
$$C(n)=\sum_{i=1}^{\infty} c_{i}(n) 10^{-i}$$ where $c_{i}(n) \in\{0,1,
\ldots, 9\},$
are the digits in decimal expansion. Now consider a real number
$$x=\sum_{i=1}^{\infty} \bar{c}_{i} 10^{-i} \in[0,1]$$
with $\bar{c}_{i} \neq c_{i}(i)$. Obviously $C(n) \neq x$ for all $n \in
\mathbb{N} .$ Hence $C$ is not onto. A contradiction.

{% endproof %}

HTML Elements

Text Formatting

This sentence is bold. This sentence is italic. Small text is for fine print. Your copy can also be _subscripted and ^{superscripted}, inserted, deleted, or highlighted. You would use a hyperlink to go to a new page. Keyboard input elements like Cmd + Shift are used to display textual user input.

This sentence is **bold**. This sentence is *italic*.
<small>Small</small> text is for fine print. Your
copy can also be <sub>subscripted</sub> and
<sup>superscripted</sup>, <ins>inserted</ins>,
~~deleted~~, or <mark>highlighted</mark>. You would
use a [hyperlink]
(https://github.com/ryanmcdermott/jekyll-latex) to
go to a new page. Keyboard input elements like
<kbd>Cmd + Shift</kbd> are used to display textual
user input.

Definition Lists

First Term

This is the definition of the first term.

Triple Integral

$\iiint_V \mu(u,v,w) \,du\,dv\,dw$

First Term
: This is the definition of the first term.

Triple Integral
: $\iiint_V \mu(u,v,w) \,du\,dv\,dw$

Blockquotes

Give me six hours to chop down a tree and I will spend the first four sharpening the axe. — Abraham Lincoln

> Give me six hours to chop down a tree and I will spend the first four
sharpening the axe.
<cite>— Abraham Lincoln</cite>

Tables

|Header 1|Header 2|Header 3|
|--- |--- |--- |
|Description 1|Description 2|Description 3|
|Description 1|Description 2|Description 3|
|Description 1|Description 2|Description 3|

Images

{% include image.html
    url="/assets/latex_image_example.jpeg"
    description="Mountain landscape by John Towner."
%}

Lists

Unordered List

• List Item 1
• List Item 2
• List Item 3

Ordered List

1. List Item 1
2. List Item 2
3. List Item 3

### Unordered List
- List Item 1
- List Item 2
- List Item 3

### Ordered List

1. List Item 1
1. List Item 2
1. List Item 3