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Apr 26, 2026

If 0.999... equals 1, what about 0.999...8?

If 0.9‾=10.\overline{9} = 10.9=1, then does 0.8‾=0.9‾0.\overline{8} = 0.\overline{9}0.8=0.9?

Wait no thats dumb. But hear me out:

If 0.999...=10.999... = 10.999...=1, then what about 0.0999...0.0999...0.0999...? Is that 0.10.10.1?

And what about 0.999...80.999...80.999...8? Like infinite 9s then an 8 at the "end"? I know there is no end but someone on Reddit was saying this is how surreal numbers work and now im confused.

Also: does 1.0‾11.\overline{0}11.01 exist? Like 1 point infinite zeros then a 1? My brain hurts.

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1 Answer

0
Emily Park
Emily Park
Apr 27, 2026
Accepted
In ordinary decimal notation, there is no decimal like $$0.999\ldots 8.$$ The dots mean the 9s continue without a final position. If there is no final position, there is nowhere to put the 8. That is different from a long finite decimal such as $$0.999998.$$ Finite decimals can have a last digit. Infinite repeating decimals do not. So $$0.999\ldots=1$$ is not saying "there is a tiny 8 or 1 at the end." It is saying the infinite decimal is defined as the limit of $$0.9,\ 0.99,\ 0.999,\ldots$$ and that limit is exactly 1.
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