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this post was submitted on 27 May 2024
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no, not really. In engineering math, sure but theoretical math it's not
0.999… = 1 in theory also.
Otherwise, there exists a δ such that 1 - δ = 0.999…
Then, the δ should have a first nonzero digit. Let us say it is in the millionth placd. But then, 0.999… cannot have a 9 in the millionth place.
Even in theoretical math, 0.999 repeating ends up being exactly equal to 1. In fact, any terminating decimal can be rewritten in a similar manner. For example, 0.25 is exactly equal to 0.24999999 repeating
It is in theoretical math as well. I just woke up and don't know the proof by heart but there is a proof for 0.99 repeating being true equal to 1.
What's 3 * 1/3? What's 3 * 0.3333333...?