In here are the list of things I did for a particular hour or day. Also included here are the screenshots of games I played, or videos I watched or listened to, or just random things I stumbled upon. I'll occasionally write down what I'm thinking, or things I'm planning to do.

• [ 2024-02-19 ]
• 18:43 [link] [context] #math

   = [(x+y)~ + -x~]y~
   = [(x+y)~-x~(x+y + -x)]y~
   = (x+y)~-x~yy~
   = -(x+y)~x~

  Okay, I'm done here for now, I don't think I could find anything further. On one hand, I now learned about the theorem x + y = xy(x~ + y~), which is what I used to solve the equation above. But then, that theorem actually uses the notion of combining two fractions together, which I was trying to avoid. Oh well.

  Here's the list of theorems that I may find useful in my tedious journey of purely using exponential notations:

   xy       = (x~y~)~
   x + y    = x(1 + x~y) = y(1 + xy~)
   x + y    = xy(x~ + y~)
   (x + y)~ = x~y~(x~ + y~)~ 
   a(x+y)~  = [a~x+a~y]~

  The last one very much looks like a function application rule that I've seen before.

  I will set aside that thought, and I will continue forth. Uhh, why am I writing like this? I have a bloody headache right now, mostly because of I ran out of coffee, and caffeine withdrawal gives me a really bad headache.

• 12:36 [link] [context] #math

  Continuing from last friday, I found about multiplicative inverses conforming to de morgan's law:

   xy~ = (x~y)~ 
   x~y = (xy~)~ 
   xy = (x~y~)~ 
  
     [1/(x+y) - 1/x]/y               
   = [(x+y)~ - x~]y~
   = (x+y)~y~ - x~y~
   = [(x+y)y]~ - x~y~
   = [xy+yy]~ - x~y~     // how do I go from this...
   = ...
   = -(x+y)~x~           // to this

  Nope, de morgan's law isn't enough. I need something like

   (x+y)~ = ~x + ~y

  What about this?

     (x+y)~ + -x~
   = -y(x+y)~x~ 
   = -(x+y)~x~y
  
  
     (x+y)~ + x~
   = (x+y)~yx~ 
  
  -------------------------
  
   = (x+y)~ + -x~
   = (x+y)~xx~ + -x~(x+y)(x+y)~
   = (x+y)~xx~ + -x~(x+y)(x+y)~
   = [ xx~ + -x~(x+y) ](x+y)~
   = [ x + -(x+y) ](x+y)~x~
   = [ x + -x -y) ](x+y)~x~
   = -y(x+y)~x~               
  
     x + y
   = xyy~ + yxx~
   = xy(y~ + x~)
  
     x~ + y~
   = x~yy~ + y~xx~
   = x~(yy~ + y~x)
   = x~y~(y + x)
  
     x~ + y
   = x~yy~ + yxx~
   = yx~(y~ + x)
  
     x + y~
   = xyy~ + y~xx~
   = y~x(y + x)
  
  
     x~ + 0~
   = x~0~(0 + x)

  0h, 0~ is undefined...

     (x+y)~
   = xy(x~ + y~)~
   = [x~y~(x~ + y~)]~
   = [(x~x~y~ + x~y~y~)]~
   = [(x~2y~ + x~y~2)]~
   = [(x~2 + x~2)y~]~
   = (x~2 + x~2)~y
   = (2x~2)~y

  So close, but this is false

  Let me try again:

     (x+y)
   = xy(x~ + y~)
  
     (x+y)~
   = x~y~(x~ + y~)~
  
     (x+y)~
   = x~y~(x~ + y~)~
  
     (x+y)~
   = [ xy(x~ + y~) ]~
   = [ xyx~ + xyy~ ]~
  
     (x+y)~
   = [xy(x~ + y~)]~
   = xy(x~ + y~)]
  
  
     1/(x+y) - 1/x               
   = (x+y)~ + -x~                // (A)
   = (x+y)~xx~ + -x~(x+y)(x+y)~
   = (x+y)~xx~ + -x~(x+y)(x+y)~  // common: x~,(x+y)~
   = [ xx~ + -x~(x+y) ](x+y)~
   = [ x + -(x+y) ](x+y)~x~
   = [ x + -x -y) ](x+y)~x~
   = -y(x+y)~x~                 
   = -(x+y)~x~y                 //  (B)

  --------------

  Welp, this sucks, I feel like I'm going in circles. I should write and separate the equations that are shown to be true first.

• 11:29 [link] [context]

  I just finished breakfast, which is quite late for a reason. Around hour ago, my husky dog went through a hole in the wall, and was set free in the swampy wilderness. I didn't realize though until I saw two people in the swap yelling to me about our dog attacking their ducklings. I said, that can't be, all of our dogs are in the house. Then I went around and noticed I don't see the big ole furry dog anywhere. Oh fuck, I thought.

  I didn't really have any choice though, but to go out and search for my dog. I screencaped a google map and annotated it to make it easier to explain.

  - In the image, the husky dog went through a hole on (B) I really don't want to wade through the swamp if possible, so I went through the front gate first (F) - I walked around neighbourhood street first (1) and (2) and didn't see any husky dog - I checked out the aggrived duckling owners, went through their lot (3) and walked through the swampy terrain. I didn't see or hear anything. - At this point, I went back inside and put some long pants and boots, because the swamp likely consists of various nasty household gooey waste, not to mention the possible snakes. - It's hard to see anything because of the really, realy tall grasses, so went to the discontinued road for a better view of the surroundings (4) - Walking through the abandoned road wasn't any easier, but at least it was dry. It had a lot of sharp tall grasses (wild sugarcane I think they are called), so I only tried walking on the edges. (5) - My mother was on a tricycle yelling, searching for me and the dog (C) - While I was on the way to (6), I heard a splash in the swamp, followed by chickens flying. From point (C) looking at point (A), I finally found the the husky dog - I slowly trudged back to point (A), hoping the husky dog didn't run off to somewhere. Thankfully, the husky was still there standing, waiting for chickens to munch on. I put him on a leash, and made our way back to the dry lands. (7) - I saw a dead orange tabby cat (A), which suspiciously looked like our cat, but I'm not sure. I didn't check further though, because the husky might actually try eating it.

  And there, it was quite a terrible morning to start a day with, but I'm just glad I found the husky safe. Worse case scenario, my dog went further out, in the neighbouring streets, never to be found again. I admit, I did kind of enjoy walking in the swamps, just the like old days.

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