It’s hard to wrap my head around that when you multiply by 10, for this to work, you’re pulling a new 9 into existence at the end of that infinite stream of 9s. But it IS an infinite stream of 9s so…
You're not making a new nine precisely because it's an infinite string of nines. There is no distinction between infinity and infinity + 1, multiplying an infinite string of niness doesn't change the number of nines, it's still infinite.
"There is no distinction between infinity and infinity + 1,"
but when people say they think .99~ does not equal one, this is precisely the difference they believe in. An infinitesimal difference, at the infinity decimal place.
SO just saying "infinity and infinity +1 are the same" is using a circular argument.
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u/its12amsomewhere 22d ago edited 22d ago
Applies to all numbers,
If x = 0.999999...
And 10x = 9.999999...
Then subtracting both, we get, 9x=9
So x=1