FWIW I never thought that functions without closed form expressions were considered elementary functions, but i guess one could choose to allow this if they wanted

Not without some form of limit process or construction. You can approximate e with the basic arithmetic operations but not actually get an exact form in finite steps. And you definitely cannot transverse an infinite binary tree, so the main point of the result in the article is missed by your arguments.

Again, you are mixing separate things. Nobody said that eml is some way to approximate elementary functions more efficiently. It is a way to express elementary functions in a finite amount of operations. Meaning, computing symbolically, not numerically. Eg I may care that exp(3)*exp(2)=exp(5) without caring to approximate exp(5) numerically. The paper is literally under "Computer Science > Symbolic Computation", not "numerical analysis" or "engineering" after all.

And to be precise:

> Go ahead and show how to compute exp or ln without an infinite series without circular reasoning. You can’t, since they’re transcendental.

You don't necessarily need "infinite series", you need some limit process. A basic example is that exp(x) can be approximated by (1 + x/n)^n for large n. For the logarithm you can use a formula involving the arithmetic–geometric mean which you can approximate using an iterative process/recursion without infinite series. You can also approximate the exponential by using Newton's method together with that, see [0].

[0] Fast Computations of the Exponential Function https://link.springer.com/chapter/10.1007/3-540-49116-3_28

Moreover, the point is not always numerical computation. I don’t think anybody argues that eml sounds like an efficient way to compute elementary functions numerically. It may or may not still be useful for symbolic computations.

The article is about producing all elementary functions, which 1/(x-y) clearly doesn’t, as it doesn’t produce any transcendental function. Like many of such universality-style results it may not have practical applications, but may still be interesting on its own right.

Moreover, with a basic setup, for the most part obsidian can be replaced by almost any text/markdown editor, so no lock in, nor security risks from using community plugins.

Apart from notetaking I also use obsidian to create slide presentations, which is probably one of the laziest ways to make presentations that look good enough.

Is it only for mobile browsers? The article makes it sound [0] as if it is a general thing, even when sharing through bluetooth, and that only copying the image via usb connection allows you to keep geolocation in exif. Not sure what happens when you upload to native apps, eg to some cloud storage app (photo specific or not). I definitely want my location to stay when I make a cloud backup of my photos with an app intended for that.

[0] Quote:

>> Using a "Progressive Web App" doesn't work either. So, can users transfer their photos via Bluetooth or QuickShare? No. That's now broken as well. You can't even directly share via email without the location being stripped away. Literally the only way to get a photo with geolocation intact is to plug in a USB cable, copy the photo to your computer, and then upload it via a desktop web browser?

eml(1,eml(x,1)) = e - x

Which then if you iterate gives x (ie is inverse of itself).

eml(1,eml(eml(1,eml(x,1)),1)) = x

Because of how exp and log turn addition into multiplication and vice versa, once you have the one, you get the other easily.

and

eml(eml(1,x),1) = e^e * x

Sounds more like an actual bug than a decision to change the keyboard layout, if this happens only in the passcode screen?

I would say that for a significant part of the current market open-source models are good enough to fill a part of it.