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| Topic | Proof that 0.999...=1 |
| Cheese_Crackers 06/02/17 10:26:23 PM #63: | G_G posted... thats not what i mean What do you mean by .999...8? An infinite sequence of 9s followed by an 8? That doesn't exist because then the sequence of 9s isn't infinite. The fact that .999...=1 isn't because of rounding up. It's true that .99999999 would be rounded up to 1 in most circumstances, but .999... is a different creature. It's the difference between a finite string of 9s and an infinite one. The only way to talk about an infinite beast like .999... equaling anything is to consider what happens with an extremely long but finite string of 9s, and try to notice a value that these numbers become closer to. In this case, we would consider the following list: .9 .99 .999 .9999 .99999 .999999 .9999999 ...and so on. Maybe you can see that these values, with each iteration, are becoming arbitrarily close to 1. Of course no entry in this list will be 1, but if you want to consider the "limit" of the list - that is, an infinite string of 9s - then you need to consider what value the list entries are becoming arbitrarily close to. --- Though the fear of death is a common one, the fear of life is a more rational one. ... Copied to Clipboard! |
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