Does 0.999…∞ Equal 1?


Imagine you fill a glass with exactly one litre of water. If you pour this glass of water into three smaller glasses and make sure the amount in each of the three glasses is exactly the same, every glass would contain 0.333…∞ litres. If you pour the contents of these three glasses back into the bigger glass, you would still have one litre of water. Just keep in mind that 0.333…∞ does not terminate, and neither does 0.999…∞ Ever.

The formal calculation would be:

x = 0.999…∞
10x = 9.999…∞
10x – x = 9.999…∞ – 0.999…∞ = 9
9 = 9x
x = 1

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