Decided I need a spot to hold info I keep forgetting. Such as...

1 Image/inverse image inclusions

f-1(f(U))	⊃ U	(equality holds if injective)
f(f-1(V ))	⊂ V	(equality holds if surjective)

Finally.... fucking finally.... after years... Over half a decade comprising of my pathetic excuse for self-learning math, where I forget these simple babby's inclusions every fucking time, and EVERY FUCKING TIME I NEED THEM, I HAVE TO FUCKING SIT THERE AND DRAW THE STUPID FUCKING CHILDISH SET DIAGRAMS AND SPEND 5-10 MINUTES FUCKING REDERIVING THEM EVERY FUCKING MOTHERFUCKING TIME BECAUSE WHEN I FUCKING WRITE IT DOWN IN MY NOTEBOOK OBVIOUSLY I CAN'T FUCKING FIND OUT WHERE THE FUCK I WROTE IT A WEEK LATER SO I HAVE TO DO THE WHOLE FUCKING THING OVER AGAIN FUCK FUCK FUCK FUCK FUCK. Well now it's finally fucking typed out and accessible on-the-go. Oh look at that I TYPED THE WRONG FUCKING THING AND FUCKED IT UP AGAIN (edit: just fixed it... I think... I FUCKING THINK. I DON'T KNOW WHY THESE FUCKING BABBY INCLUSIONS FUCK MY BRAIN UP SO FUCKING MUCH. WHEN I REDERIVE THEM I HAVE TO FUCKING SIT THERE LOOKING AT MY STUPID FUCKING DRAWINGS LIKE SOME FUCKING SCIENTIST LOOKING AT A BACTERIA CULTURE THROUGH A FUCKING MICROSCOPE WHEN IT SHOULD TAKE 30 FUCKING SECONDS TO FIGURE THE WHOLE FUCKING THING OUT BUT IT JUST FUCKING BREAKS MY BRAIN SO I'M FUCKING STUCK THERE IN FUCKING LIMBO WHILE EVERYONE ELSE IS MAKING PROGRESS IN LIFE RISING UP THE CAREER LATTER GETTING INTO HEALTHY RELATIONSHIPS COOKING GOOD FOOD AND SPENDING THEIR TIME WELL AND FUCKING ACTUALLY DOING FUCKING THINGS WITH THEIR LIFE THAT HAVE TANGIBLE FUCKING PROGRESS INSTEAD OF FUCKING RUNNING INTO THE SAME FUCKING MATH PROBLEM FOR OVER 5 YEARS AND NOT FUCKING DOING THE OBVIOUS THING TO FUCKING FIX IT BECAUSE I'M THE SORT OF PERSON THAT WILL MAKE THE SAME FUCKING MISTAKE OVER AND OVER AND OVER AGAIN AND THE 300TH TIME MAYBE.... JUST FUCKING MAYBE I'LL LEARN. BUT BY THAT TIME, IT'S TOO LATE ISN'T IT? AFTER YOU FAILED 300 TIMES IN A ROW, WHO FUCKING CARES IF YOU SUCCEED THE 301ST TIME IF YOU'RE ALREADY 300 STEPS BEHIND. YOU'RE FUCKED. YOU'RE ABSOLUTELY FUCKED IN LIFE, MOTHERFUCKER). Well, after years, I've finally learned my lesson and made a page with these inclusions. May it serve me well.