Ciro Santilli @cirosantilli 35

A good definition is by using Dedekind cuts.

All of them need a vacuum because you can't shoot elecrons through air, as mentioned at Video "50,000,000x Magnification by AlphaPhoenix (2022)".

It is true that one image is worth a thousand words, but unfortunately it is also true that one image takes up at least as much bytes as a thousand words!

Having one single page to rule them all is of course the ideal setup for a website, as you can Ctrl + F one ToC and quickly find what you want.

And, with Linux Kernel Module Cheat Ciro noticed that it is very hard to write so much intelligent prose that becomes larger than reasonable to load on a single webpage.

He then started using this technique for everything he writes, including this page and Chinese government.

However, if there are too many images on the page, the loading of the last images would take forever in case users want to view the last sections.

There are two solutions to that:

Ciro is still deciding between those two. The traditional approach works for sure but loses the one page to rule them all benefits.

The innovative approach will work for interactive viewing, but archive.org will fail to load the images for example, and there may be other unforseen consequences.

Wikimedia Commons is awesome and automatically converts and serves smaller versions of images, so always choose the smallest images size needed by the output document. Readers can then find the higher resolution versions by following the page source.

This also comes to mind: motherfuckingwebsite.com

zettelkasten.de/posts/overview/ from zettelkasten:

Website: www.theoremoftheday.org/

A linear map is a function $f:V_1(F)\to V_2(F)$ where $V_1(F)$ and $V_2(F)$ are two vector spaces over underlying fields $F$ such that:

A common case is $F=\mathbb{R}$, $V_1={\mathbb{R}}_m$ and $V_2={\mathbb{R}}_n$.

One thing that makes such functions particularly simple is that they can be fully specified by specifyin how they act on all possible combinations of input basis vectors: they are therefore specified by only a finite number of elements of $F$.

Every linear map in finite dimension can be represented by a matrix, the points of the domain being represented as vectors.

As such, when we say "linear map", we can think of a generalization of matrix multiplication that makes sense in infinite dimensional spaces like Hilbert spaces, since calling such infinite dimensional maps "matrices" is stretching it a bit, since we would need to specify infinitely many rows and columns.

The prototypical building block of infinite dimensional linear map is the derivative. In that case, the vectors being operated upon are functions, which cannot therefore be specified by a finite number of parameters, e.g.

For example, the left side of the time-independent Schrödinger equation is a linear map. And the time-independent Schrödinger equation can be seen as a eigenvalue problem.