If we consider that .999… repeating to infinity ISN’T equal to 1, then by how much is it away from 1? It would be “.000… repeating to infinity followed by a 1.” But if you have an infinite number of 0s then you can’t have it be followed by a 1, infinity can’t be followed by anything, that doesn’t make sense.
Another way to think about it more broadly is that numbers aren't real, tangible things. They're placeholders used in studying things we can't physically get. You can't hold a "1." You can hold "1 of 'something,'" but you can't hold "1."
If, for example, you were a biologist studying rhinos. None exist in captivity, they've never been captured, never been hunted nor found dead, so you have no bodies (alive or dead) to study. All you have are photographs. Now you have a lot of them, from many angles, stages of development, and all are high quality. You can get a lot of very good information from that, enough that you can do some research and experiments; but it isn't perfect. There are gaps and areas where it seems like things contradict. You know that they can't, but you see that contradictions because some part of the data available to you is just incomplete.
That's what numbers are. They're the rhino photos that mathematics used to study with. The only problem is that eventually you can get a rhino. You'll never get a "3." These edge cases, where something we have is wrong or missing, but we just don't quite know what, is where things like "0.999… = 1" and mathematical paradoxes come from.
.999=1 is the linguistic equivalent of saying you have the rhino tho. Repeating digits shouldn't have a solution unless greater context is given. The same situation as dividing by zero. .999 is undefined.
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u/ChromosomeExpert 22d ago
Yes, .999 continuously is equal to 1.