How to blog Maths in Latex

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How to blog Maths in Latex

Math Blogging Made Easy

Hi, do you want to blog about Mathematics, but are wondering how is it possible to write equations and formulae and render them as in Latex?
Don’t worry, all the hurdles have been resolved and there is a pretty easy way to blog about mathematics. So without further ado, here is the recipe:

  1. Create your blog on Blogger.
  2. Open the site StackEdit and go to its app/editor.
  3. Connect your google account with StackEdit.
  4. Read some of the markdown features on the Welcome Page.
  5. Then create your own StackEdit document with the title that you want for your blog post. (You can write all mathematics equations using tex support in StackEdit).
  6. Now go to Menu in the right sidebar. Click on Publish.
  7. You have the option to add Blogger account.
  8. After adding your Blogger account, you can post your StackEdit document either as a blog-post or as a blog-page.
  9. Before publishing you can add your labels/tags/categories to this document in the file properties (in Menu on right side bar).
  10. In Publish option in the menu, you can click on either publish to Blogger or to Blogger Page.
  11. In the pop-up window, write the blog url (the blog you had made a publishing account in point 7 above).
  12. Choose Styled HTML template.
  13. Now press OK and there you go!

But, wait we haven’t added any mathematical equation to show off!
Here are some:

Characteristic Function

1.0 Characteristic function of a set E⊆ΩE\subseteq\Omega is a mapping XE:Ω→{0,1}\mathcal{X}_E:\Omega\to \{0,1\} defined as
XE(x)={1, if x∈E0, if x∉E \mathcal{X}_E(x) = \begin{cases} 1, \text{ if } x\in E \\ 0, \text{ if } x\notin E \end{cases}
And, here is a nice proof, how it looks:

Archimedean Property

2.0 For every x∈Rx\in\mathbb{R}, there exists nx∈N∗n_x\in\mathbb{N}^*, such that x<nxx< n_x,
i.e., the set N\mathbb{N} is NOT upper-bounded in R\mathbb{R}.
Proof: (contradiction approach): Let there exist x0∈Rx_0\in\mathbb{R} such that, ∀n∈N,n≤x0\forall n\in\mathbb{N}, n\le x_0.
⟹x0\implies x_0 is an upper-bound of set N⊂R\mathbb{N}\subset \mathbb{R}.
⟹∃α∈R\implies \exists \alpha\in\mathbb{R}, such that α=sup⁡N\alpha=\sup{\mathbb{N}}.
Now, α−1<α\alpha-1<\alpha, so α−1\alpha-1 is not an upper-bound of N\mathbb{N}.
⟹∃m∈N\implies \exists m\in \mathbb{N}, such that α−1<m\alpha-1 < m.
⟹α<(m+1)\implies \alpha<(m+1) for some (m+1)∈N(m+1)\in\mathbb{N}, (thanks to Peano)
which contradicts the fact that α=sup⁡N\alpha = \sup{\mathbb{N}}.

Happy Maths Blogging! ;-)

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