| Off Topic > Off Topic |
| the ultimate question: does 0.9999... equal 1 |
| << < (7/7) |
| SetGaming:
--- Quote from: TableSalt on March 18, 2017, 08:13:15 PM ---Okay, so is this 0.999... (infinite 9s here) ...999 or is it 0.999... (infinite 9s here, with no literal end) --- End quote --- literal no end |
| Blockomaniac:
nerds |
| Shift Kitty:
Here's an idea... Let's get rid of the decimal system. |
| Ipquarx:
In the set of real numbers, 0.9999... = 1. In the set of hyperreals where you can have numbers infinitely close to but not equal to 1, 0.999... is not a valid representation of a number as far as I'm aware. So yes, it's equal. If you want some ideas of why, here are a couple proofs: x = 0.9999... 10x = 9.9999... 10x - x = 9.0 9x = 9 x = 1 1/9 = 0.1111... 2/9 = 0.2222... 3/9 = 0.3333... ... 7/9 = 0.7777... 8/9 = 0.8888... So 9/9 = 0.9999..., and 9/9 = 1. |
| Texan101:
Easy solution. .999... - 1 = What? 0.000.... Never has a 1 or higher, so it gets simplified to 0. |
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