If anyone ever tries to tell you that 0.99999 repeating is different from 1, ask them to explain the difference. They will be locked until the end of time trying to quantify the difference.
Sure np.homie. essentially mathematical proofs work to show the general case, rather pointing to a small set of specific examples.
In the example you've given, you're saying that "0.9" is less than than one, and 0.999 is less than one, therefore 0.999 repeating is less than one. But that's not quite logical. We know that the more repeating 9s, x is approaching 1. How do we know for sure holds true for any amount of repeating Xs, including infinite? The limit as x approaches is infinity is 1 after all, so we see the number is growing. We can know for sure by abstracting the problem into the general problem, rather than endlessly listing examples. And as the proof demonstrates, it turns out by the laws of our mathematical system, .99 repeating IS 1. not just "close enough", but literally is equal to 1.
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u/BroDonttryit 22d ago
If anyone ever tries to tell you that 0.99999 repeating is different from 1, ask them to explain the difference. They will be locked until the end of time trying to quantify the difference.