3 ms·

Here is a comment where I tried to clarify, but yes you seem to basically understand my point: https://news.ycombinator.com/item?id=23007600 https://news.ycomb

Here is a comment where I tried to clarify, but yes you seem to basically understand my point: https://news.ycombinator.com/item?id=23007600 https://news.ycombinator.com/item?id=23007600

ColinWright 7y ago
My personal experience is that people want to argue from intuition about what 0.9999... means, and when you try to make it precise they say that it's obvious. Then they derive all sorts of nonsense and conclude that mathematics is all rubbish. If someone really wants to understand it then I'll explain current mathematical thinking, including non-standard analysis and the surreals. But most people don't want to put in the work to understand how these issues have been resolved, and just want to argue from their intuition.
- CogitoCogito 7y ago
  Someone else here brought up the surreal numbers and my intuition says that it's right to do that. The various arithmetic proofs thrown around here don't explicitly make use of completeness. As such they should be correct proofs in the surreal numbers as well. But they basically are not. Here is a blog post about it: https://thatsmaths.com/2019/01/10/really-0-999999-is-equal-to-1-surreally-this-is-not-so/ https://thatsmaths.com/2019/01/10/really-0-999999-is-equal-t... I don't quite know how to formalize it, but I'm pretty certain that if these proofs logically worked (in the "theory of proofs sense"), then they should work in the surreals as well. Anyway it's just intuition. My main point in this thread is that I don't really accept the proofs of this that don't use completeness as a step. Though I do suspect that proofs not making use of it are actually incorrect proofs in their own right. If I were curious enough I'd think back about formal proofs and models and all that jazz, but I probably already have spent more time in this thread than I should. :) edit: The more I think about it I feel like someone actually explained to me this (i.e. why this proof is wrong using surreals as reasoning) a long time ago and I'm just remembering echos of it in my mind. Wish I could remember something more useful...or that I were a logician...

Here is a comment where I tried to clarify, but yes you seem to basically understand my point: https://news.ycombinator.com/item?id=23007600 https://news.ycombinator.com/item?id=23007600

ColinWright 7y ago

My personal experience is that people want to argue from intuition about what 0.9999... means, and when you try to make it precise they say that it's obvious. Then they derive all sorts of nonsense and conclude that mathematics is all rubbish. If someone really wants to understand it then I'll explain current mathematical thinking, including non-standard analysis and the surreals. But most people don't want to put in the work to understand how these issues have been resolved, and just want to argue from their intuition.

CogitoCogito 7y ago
Someone else here brought up the surreal numbers and my intuition says that it's right to do that. The various arithmetic proofs thrown around here don't explicitly make use of completeness. As such they should be correct proofs in the surreal numbers as well. But they basically are not. Here is a blog post about it: https://thatsmaths.com/2019/01/10/really-0-999999-is-equal-to-1-surreally-this-is-not-so/ https://thatsmaths.com/2019/01/10/really-0-999999-is-equal-t... I don't quite know how to formalize it, but I'm pretty certain that if these proofs logically worked (in the "theory of proofs sense"), then they should work in the surreals as well. Anyway it's just intuition. My main point in this thread is that I don't really accept the proofs of this that don't use completeness as a step. Though I do suspect that proofs not making use of it are actually incorrect proofs in their own right. If I were curious enough I'd think back about formal proofs and models and all that jazz, but I probably already have spent more time in this thread than I should. :) edit: The more I think about it I feel like someone actually explained to me this (i.e. why this proof is wrong using surreals as reasoning) a long time ago and I'm just remembering echos of it in my mind. Wish I could remember something more useful...or that I were a logician...