# Mathjax is now supported

The tex2jax preprocessor defines the LaTex math delimiters, which are
`\\(...\\)`

for in-line math and `\\[...\\]`

for displayed equations. It also
defines the TeX delimiters `$$...$$`

for displayed equations, but it does not
define `$...$`

as in-line math delimiters. We can change that, but I don’t want
to, because they had a reason to do so, and I think it easy to understand
what is it.

I like to use this tool to help me write LaTex expressions.

Very nice, let’s try this

```
\\[\frac{10^{120}}{10^{106}} = 10^{120-106} = 10^{14}\\]
```

\[\frac{10^{120}}{10^{106}} = 10^{120-106} = 10^{14}\]

Volume of a ball

```
$$\int_{\varphi=0}^{\pi}\int_{\theta = 0}^{2\pi}\int_{r=0}^{R}r^2\cdot\sin{\phi}\cdot d r \cdot d \phi \cdot d \theta = \frac{4}{3} \pi R^3$$
```

Let’s say we want to add a little bit of inline math

## Support Vector Machine

We try to separate positive from negative examples.

```
^
|\ \ +
| \ \
| \ \ + +
| - \ \ + +
|- - \ \ +
| - - \ \ +
|______\__\_________
```

Let \(\mathbf{w}\) be a normal vector of the street, and \(\mathbf{x}\) a vector pointing to a sample. If we project \(\mathbf{x}\) on \(\mathbf{w}\), we obtain the scalar :

\[p = \frac{\mathbf{x} \cdot \mathbf{w}}{|| \mathbf{w} ||} = || \mathbf{x} || \cdot \cos(\mathbf{x},\mathbf{w})\]

\(\mathbf{w}\) is always the same, so its norm \(|| \mathbf{w} ||\) is constant. So our problem can be written as :

\[\mathbf{x} \cdot \mathbf{w} \geqslant C\]If \(\mathbf{x} \cdot \mathbf{w} \geqslant C\) where is C is a constant then the sample x is a positive element, otherwise, it is a negative one. If we let b = -C, we can rewrite this :

\[\mathbf{x} \cdot \mathbf{w} + b \geqslant 0\]This is what we call the DECISION RULE.

\[\begin{align*} \mathbf{w} \cdot \mathbf{x_+} + b \geqslant 1 \\ \mathbf{w} \cdot \mathbf{x_-} + b \leqslant -1 \end{align*}\]
{Software Engineer, Developer, AI enthusiast, I like to build stuff}