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I meant the article suggested it only becomes a ring after you add b*sqrt(5) part. But yeah, I'm nitpicking.
by ajuc 9y ago
I meant the article suggested it only becomes a ring after you add b*sqrt(5) part.
But yeah, I'm nitpicking.
- richard_todd 9y agoI’m not sure if this is what you are missing, but: Rings are closed, so you have to add an infinity of new numbers, not just the literal sqrt(5). a + b*sqrt(5) is a convenient way to denote that all those numbers are in your system. So in some sense, once you’ve decided to incorporate sqrt(5), it really is only a ring once you add that part. Obviously there are tons of rings that have nothing to do with this recipe... maybe that is your nitpick?
- soVeryTired 9y agob * sqrt(0)? But yeah, the integers form a ring in their own right. They call the new system a ring, but that doesn't mean the old system wasn't also a ring. Also not all rings are of that form - as you say a ring is a very general algebraic structure.