My favourite math fact is that 0.9999999.. is equal to 1. Exactly. Not approximately. Not as a rounded number. 0.9999 (recurring) is exactly 1.
Question. How the fuck does that work?
I tried explaining it here:
Here’s another perspective on why .999… repeating is exactly equal to 1.
For any two distinct real numbers, we can always find a rational number strictly between them, i.e. that rational number must be able to be expressed as a terminating decimal or a repeating decimal. To be clear, that rational number is strictly between the two values; it is not allowed to be equal to either.
Suppose k is a rational number strictly between 1 and 0.9999…. If this is possible, then, I can write k exactly as either a decimal with finite digits, or I can write k as a repeating decimal. The problem is, there are no decimals with finite digits between 1 and 0.999… , and there is no way to write a repeating decimal that is greater than 0.999… and still less than 1. Either way, a k strictly between 1 and 0.999… does not exist. The only way this can be true is if those two numbers are not actually distinct. That is to say, 1 = 0.999…..
i truly appreciate how math seems like it’s this infallible always-true only-one-answer thing, when in reality math is just like:
So the thing about the bathroom renovation/massive pipe repair in our house is that it’s been this insurmountable wall in front of me for the entirety of this year (it was supposed to start as early as in January but another covid outbreak postponed it until April). It’s had me tied both financially and mentally - for instance, I’ve been unable to look for a more suitable job as the renovation has made me unable to live in my own house for several days at a time. It’s just been a lot. But today I found myself thinking about the future for the first time in months, and it really… It’s like that sunny spring day euphoria all over again. Like I’ve been in survival mode for over two months and now it’s finally letting up.
Ralsei is such an interesting case study in “you can take this story at face value, at what’s the most comforting, at what gives you the warm fuzzies, but in doing so you’re ignoring the people - including yourself - that this story dehumanizes in order to function”.
Currently channeling all of my mental energy into casting the spell of Tomorrow The Asbestos Removal Guy Manifests In Fooey’s House Precisely At 7 AM And Starts Working Swiftly And Efficiently
HOLY SHIT HE’S ACTUALLY HERE AND PRECISELY AT 7 AM I’M A WITCH I AM A GOT DAM SORCERER
Currently channeling all of my mental energy into casting the spell of Tomorrow The Asbestos Removal Guy Manifests In Fooey’s House Precisely At 7 AM And Starts Working Swiftly And Efficiently
Huge pet peeve in video games is when you can’t hold your breath underwater for very long or it takes a good while to regain your breath above water. Unrealistic. Like my condolences to the devs for your lack of breath support but that just could not be me…
Just THINK. If Chuck was born the only heir to George Hamlin. No competition for achievement, a parent that would’ve acknowledged and rewarded Chuck’s acumen and accomplishments. Chuck Hamlin would’ve made his father so proud, and done him right. He marries a sophisticated wife that admires his achievements, likes to have her accomplished husband on her arm at fundraisers, and doesn’t feel diminished because he is not an emotional man, and doesn’t crumble in a way she can’t connect with.
Think of how Howard would’ve LAPPED up McGill Snr’s ethos. Be kind to others above all else. Think of Howard in that lonely house with Cheryl. And compare it to Howard McGill, big brother of Jimmy McGill. How would he have LOVED Jimmy’s adoration? Jimmy’s insistence on being brothers and always being there for each other? He nicknames him Charlie Hustle. He forgives his indiscretions. He sees the positives in his behaviours. He smiles at the chance to work with Jimmy. And he marries a kind-hearted violinist who loves him for himself, and supports him even when he is at his lowest.
I’m not saying the parallels have to be exact. But it is interesting to think about.
you’re seeing a breaking bad concert. everyone is having a great time. walter seems a little excited. “we have a surprise for you guys.” jesse says. all the sudden saul goodman comes out and starts singing the breaking bad remix. when saul gets to my daddy and my mommy, someone else starts singing. “you are not the guy you’re not capable of being the guy i had a guy but now i don’t you are not the guy.” Lights flash everywhere and you see walter and jesse singing my daddy and my mommy along with saul while mike sings you are not the guy. Everyone in the crowd is going wild and starts crying. Then if things couldn’t get any better, gus and max walk onto stage and kiss, holding the gay flag.
