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    1. Useless stuff
      1. More useless stuff
    2. Useless LaTeX
    3. References

This past Christmas and new year season has been the most restful for me in recent memory: coming off the backside of the pandemic, making a career change, and moving across the country has occupied me the last few years. In this time, I've been trying to take better care of myself, seeing the doctor, etc. on things that have been bothering me but I've been putting off.

During this time, I've been reading a lot of essays that get shared on Hacker News that I've been finding quite insightful and inspiring. One in particular was written in the form of a letter to their younger self with a lot of advice and introspection that I found extremely relatable, and partly inspired me to write this up; instead of a letter to my past self—I don't think I'm quite there yet—I thought I would write this up in the spirit of new year's resolutions, and serve to remind myself of more mindful times as the year inevitably picks up.

Useless stuff

Definition (Interior and Closure):\textbf{Definition (Interior and Closure):} Given a subset SS of a topological span XX, the interior\textit{interior} of SS is in XX, denoted intX(S)\text{int}_X(S), is defined as the union of all open sets contained in SS, and the closure of S in X\textit{closure of }S\textit{ in }X, denoted clX(S)\text{cl}_X(S), is defined as the intersection of all closed sets containing SS.

More useless stuff

a=b+c=e+f \begin{split} a &=b+c\\ &=e+f \end{split}
WOW definition 1 is pretty cool! Sidenotes are cool! Ok[1]

[1] but footnotes are cooler! Agreed!
I think we should really consider the works of (Baveja (2024), Chakraborty et al. (2024)) because they're cool! Don't forget (Singh et al. (1996)) now.

Useless LaTeX

Rn=∑t=nTγt−nr(st,at) R_n=\sum\limits_{t=n}^T \gamma^{t-n} r(s_t,a_t) φ(E[X])≤E[φ(X)]. \varphi(\mathbb E\left[ X\right]) \le \mathbb E\left[ \varphi(X)\right]. exp⁡(iπ)+1=01+1=2\begin{array}{rcl} \exp(i\pi)+1 &=& 0\\ 1+1 &=& 2 \end{array} exp⁡(iπ)+1=01+1=2\begin{aligned} \exp(i\pi)+1 &= 0\\ 1+1 &= 2 \end{aligned}

but (3) is fine.

References

Gunbir Singh Baveja. Website built with Franklin.jl and the Julia programming language.