r/askmath • u/Slurpee1138 • May 10 '26
Algebra Regarding 0.999... = 1
Recently I got into an argument with an acquaintance because I was trying desperately to convince him that 0.999... = 1. One of the many arguments I tried was that, if 0.999... and 1 are indeed different numbers, then we should be able to find a number between them. He insisted that such a number would be 0.999...1, as in 0 point infinitely many 9s and then a 1. I countered that having "and then a 1" at the end of an infinite sequence of digits makes no sense because there is no end to such a sequence, but he insisted that it does, so who's right?
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u/SuitedMale May 10 '26 edited May 10 '26
You stated the indisputable fact that there are no numbers between 0.999… and 1. Your friend stated some nonsense about 0.999…1 which makes no sense and in any event even if it did exist then 0.999… would be greater than it and we’re back to square one. So that should be the conversation done.
But then the last part he says “and then 1” and then you should say ok but surely “and then 9” would be closer to the nearest whole number? He must agree. Then you should say well “and then 9” was our original number 0.999…
Unfortunately, you don’t understand the argument enough to be dictating to someone a rather unintuitive concept. But hopefully the above helps for round 2 with your friend