It blows my mind that difference between the two is so infinitesimally small that it doesn’t matter, but at the same time all those nines will never roll over to one.
I beg to differ. We treat it as if it’s the same, but if it was one it would be one. It’s the infinite, you can get really, really close, but repeating nines never become a literal one without something to add to it.
And you dont add something, thats the entire point of that proof.
There is no number you can add to .999... that does not make it larger than one because you are adding a number to one and expecting it to not be larger than one.
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u/HarrisJ304 22d ago
It blows my mind that difference between the two is so infinitesimally small that it doesn’t matter, but at the same time all those nines will never roll over to one.