0.9999 ≊ 1

I've got a page about this too: https://susam.net/1.html

In fact, this is the oldest blog post archived on my website! I wrote it about 24 years ago, back when pondering on questions like this felt endlessly fascinating. What especially intrigued me at the time was how the concept of limits (the epsilon–delta definition) allows us to avoid the conceptual pitfalls often associated with infinity. Using limits, we can define and understand problems like this in a precise and rigorous manner, something that felt both elegant and incredibly satisfying.

any and all arguments about infinity must include the word "believ", anything else is bombastic hubris I believe the universe to be infinite, that notion fits my own observations, and is comforting, the notion that there is more, in how ridiculous all the squabling about this and that, the who's and why's, is, and my own reduction of the idea of infinity is that in a universe with infinite, time,space, energy and matter, probability does not exist,everything must happen. Perhaps not right here and right now, I hope, as that would be a bit much, but perhaps that is a hint, and all we are is filters, tuned to the whatever it is that we talk about so much.