Abstract
This project is called jekyll-latex. It allows you to write markdown posts using the Jekyll framework with the beautiful typography of LaTeX and the MathJax library so you can render gorgeous equations like this one below: $$ J(\theta) =\frac{1}{2m} [\sum^m_{i=1}(h_\theta(x^{(i)}) - y^{(i)})2 + \lambda\sum^n_{j=1}\theta^2_j $$
{% 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
* TOC
{:toc}
Theorems, Definitions, and Proofs
The real numbers $\mathbb{R}$ are uncountable
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.
{% 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 |
|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.liquid
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
- List Item 1
- List Item 2
- 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
