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0.9999 ≊ 1
If you're playing both sides, you always come out on top.
In the end, you have a bunch of websites strongly asserting that there’s absolutely no difference between 0.9999… and 1; and a network of “number skeptics” who claim that there must be some distance separating the values, no matter how small. The rule doesn’t have any cosmic significance; it’s just that to keep things simple, we define reals as an Archimedean group devoid of infinity-related singularities. The key tidbit is that if a and b are positive reals and a < b, there must exist some finite integer x that makes a · x > b. Infinite and infinitesimal quantities don’t obey that rule, so they’re not invited to the club.
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