In the 7th-grade math class I teach, when we discussed closed and open intervals I stumbled a bit when it came to talking about 0.99999... possibly being the edge of an open interval. I told the students that for technical reasons we can't say that, and 0.99999... = 1, but to explain why would be too hard. Job Currell found out why from his brother Isaac, and we talked about it in class, which was good, but I thought I'd better write up a handout to explain this weirdness. It's something I'd never heard of myself before I was in my 50's, when Professor Christopher Connell told me about it. That handout became this Substack article.
Why 0.9999... Equals 1.0000...
Why 0.9999... Equals 1.0000...
Why 0.9999... Equals 1.0000...
In the 7th-grade math class I teach, when we discussed closed and open intervals I stumbled a bit when it came to talking about 0.99999... possibly being the edge of an open interval. I told the students that for technical reasons we can't say that, and 0.99999... = 1, but to explain why would be too hard. Job Currell found out why from his brother Isaac, and we talked about it in class, which was good, but I thought I'd better write up a handout to explain this weirdness. It's something I'd never heard of myself before I was in my 50's, when Professor Christopher Connell told me about it. That handout became this Substack article.