> On the second day, there are two gaps: “between nothing and zero” and “between zero and nothing”. Two numbers spawn in those two gaps. Call them –1 and 1.
Got lost here. I think I'm officially too dumb for math.
I think it's just we don't have a way to say/write these numbers. So you make up a way to write them (-1 and 1) and continue.
The numbers don't matter and you could replace -1 and 1 with anything. It's just easier to begin your new fake number at - 1 and 1. Because position does matter.
There has to be some procedure how to come up with "new" numbers though, if you want to have more in the end than just a fancy binary tree - in particular if you want to map your "fake numbers" to the reals, infinity, etc.
This procedure is enough. If you define addition and other operations in a certain way (as Conway did), it turns out that on the omega-th day (i.e. after initial infinite steps), all reals will be born.
howunfortunate · · focus · HN ↗
Got lost here. I think I'm officially too dumb for math.
dubcanada · · focus · HN ↗
The numbers don't matter and you could replace -1 and 1 with anything. It's just easier to begin your new fake number at - 1 and 1. Because position does matter.
xg15 · · focus · HN ↗
danabramov · · focus · HN ↗