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It isn't a limit thing, though? It is a textual representation thing. You are not confused that 01 is the same as 1. Similarly, you are ok that .33... is the
by taeric 3y ago
It isn't a limit thing, though? It is a textual representation thing. You are not confused that 01 is the same as 1. Similarly, you are ok that .33... is the same as .3... In fractions, you are ok with the idea that 1/2 is the same as 2/4. And that you are often supposed to work in reduced form, such that you will probably never put 2/4 down as an answer to any problem. We work with "regular" numbers for so much of our life that it is odd to consider how to write them to that level.
- burnished 3y agoIts not a textual representation thing, there are other repeating sequences that do not converge. I mention limits because that was the context in which I learned about this, others have pointed out you can demonstrate this with just algebra (which makes me wonder if I just wasn't paying attention when that lesson came up).