Notes on machine learning, software engineering, math, and systems.
Why Is a Limit Exact If We Only Ever Get Arbitrarily Close?
A limit, if it exists as a real number, is exact and unique and not an approximation. But books and intuitive explanations constantly talk about getting “arbitrarily close”. But being arbitrarily close still does not mean being exactly at the point, right? It is just arbitrarily close ¯\_(ツ)_/¯ So why are we allowed to use the value of a limit in calculations such as the derivative formula? And why is it that the limit is always an exact value and not just an approximation? We will try to convince even the biggest skeptic (me) that the limit is indeed an exact number and not just an approximation and answer these questions. To do this, it makes sense to look at the derivative formula, as it is relatively intuitive and offers useful insight. For the sake of simplicity, we will remain within the real-number domain and use polynomials as examples. ...
Rust Compiler Contribution
To gain more experience in software-engineering I was playing around with the thought to contribute to open-source software. Since I started reading “Programming Rust” by O’Reilly to get started with a low-level language, I got also interested in understanding what happens under the hood when we execute or compile a program. Therefore, I thought it might be a good idea to look into the Rust Programming language itself. Coincidentally, I found this video from Esteban Kuber, which ultimately made sure to check out the Rust compiler. ...