I went down the rabbithole, and as far as I can tell, you have to axiomatically assume infinities are real in order to prove Goodstein’s theorem.
I challenge the existence of ordinal numbers in the first place. I’m calling into question the axioms that conjure up these ordinal numbers out of (what I consider sketchy) logic.
But it was a really fun rabbithole to get into, and I do appreciate the elegance of the Goodstein’s theorem proof. It was a little mind bending.
I haven't studied math beyond what was needed for my engineering courses.
However, I also am starting to believe that infinity doesn't exist.
Or more specifically, I want to argue that infinity is not a number, it is a process. When you say {1, 2, 3, ... } the "..." represents a process of extending the set without a halting condition.
There is no infinity at the end of a number line. There is a process that says how to extend that number line ever further.
There is no infinity'th prime number. There is a process by which you can show that a bigger primer number must always exist.
Long time OpenBSD fan. Used it as my daily driver for years before standardizing all computers at home to macOS. I still think about going back to openBSD one day, but it's no longer very practical as a daily driver.
I want to use OpenBSD for the next project I'm building. However, I can't wrap my head around the old way of doing deployments (before containers). People who've built production grade systems with OpenBSD:
1. How do you deploy software?
2. How do you manage fleets of servers?
3. How do you spin up/turn down servers from cloud providers? (I only know of Vultr who provided an OpenBSD option out of the box).
I ended up having a work laptop that looks exactly like my personal laptop. After making an embarrassing mistake once, I picked up some stickers and stuck them on my office laptop.
Now, my work laptop looks clearly distinct, not just from my own personal laptop, but also from all the identical laptops other people at work bring to meeting rooms.
Yay! A tiny minuscule bit of my code is riding on these. While I no longer work there, I am absolutely thrilled at this milestone
1. Congratulations everyone! Yay!
2. I absolutely recommend Zoox as a great place to work. Believes me, I’ve sampled many jobs, Zoox is up there with Google in terms of what the experience feels like in my experience.
But I am interested in the monero aspect here.
Should I treat this as some datapoint on monero’s security having held up well so far?