All I know right now is it’s a fun art style to draw.

I liked using Gnome because it was my first introduction to virtual desktops. I am very thankful that it encouraged me to make use of them and to put 1 window per desktop. However, I tried KDE and it turns out that

In a nutshell I liked Gnome because it encouraged me to use KDE in a fun way. The actual thing that made me try KDE was finally getting fed up by their whole “we refuse to implement server side decorations and also a bunch of other basic features/customization stuff middle finger emoji” thing.

Don’t worry, this ends well.

I’ve got 99 problems and 99 problems is at least one of them.

May as well go through the proofs:

First, we need to establish that two infinities are equal in cardinality (aka size) if all their elements can be 1:1 mapped to each other.

So, to go from the reals within [0, 1] and [0, 2], we can multiply by 2. This maps every value within [0, 1] to every value within [0, 2], so these are of the same cardinality.

Where things get interesting is the proof that the reals within [0, 1] are of greater cardinality than every integer.

Say we have an arbitrary mapping from every integer to a real within [0, 1]:

0 -> 0.89236…
1 -> 0.47389…
2 -> 0.84776…
3 -> 0.18790…
4 -> 0.90542…
⋮           ⋱

This list contains every integer, but it does not contain every real number because we can always come up with a new one by ensuring at least one digit is different in each existing real:

0 ->  …8… ≠ 9
1 ->   …7… ≠ 8
2 ->    …7… ≠ 8
3 ->     …9… ≠ 0
4 ->      …2… ≠ 3
⋮           ⋱

          0.98803… is not within the list

Therefore, no 1:1 mapping between the integers and reals exists. Because the limiting factor is the amount of integers, the cardinality of the reals is greater than that of the integers.

Edit: https://en.wikipedia.org/wiki/Cantor’s_diagonal_argument

I recall sitting still for a while at one point and momentarily loosing the ability to make out anything but a patchwork of colors from my vision. It’s fascinating, what the mind’s processing tells us about the world compared to the either low granularity or low field of view provided by each input. I’m pretty sure I was only able to process my peripheral vision during that experience, maybe due to the amount of detail?

Vampire rule.