I know there are proofs on this but I’m not great at math, can someone dumb it down for me?
In: Mathematics
Possibly simpler explanation since the OP is struggling with assertions that look like tautologies.
IF .999… = 1 then 1-.999…=0, yes? Not asserting that .999… = 1, just saying what would be true IF IT WERE.
So what’s 1-.999…? 0.000…
It is NOT 0.000…1
The really really key point, OP, is that string of 0s doesn’t end. There is no “1” anywhere in it because you never get to the end. It doesn’t have an end. Infinity isn’t just “a really huge string of numbers with an end somewhere we can’t imagine”, it literally has no end. It can’t end with a 1 because it can’t end at all.
And 0.000… is just an inconvenient way of writing “0”.
So if 1-.999… = 0, then 1 = .999…
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