While I agree that my proof is blunt, yours doesn’t prove that .999… is equal to -1. With your assumption, the infinite 9’s behave like they’re finite, adding the 0 to the end, and you forgot to move the decimal point in the beginning of the number when you multiplied by 10.

x=0.999…999

10x=9.999…990 assuming infinite decimals behave like finite ones.

Now x - 10x = 0.999…999 - 9.999…990

-9x = -9.000…009

x = 1.000…001

Thus, adding or subtracting the infinitesimal makes no difference, meaning it behaves like 0.

Edit: Having written all this I realised that you probably meant the infinitely large number consisting of only 9’s, but with infinity you can’t really prove anything like this. You can’t have one infinite number being 10 times larger than another. It’s like assuming division by 0 is well defined.

0a=0b, thus

a=b, meaning of course your …999 can equal -1.

Edit again: what my proof shows is that even if you assume that .000…001≠0, doing regular algebra makes it behave like 0 anyway. Your proof shows that you can’t to regular maths with infinite numbers, which wasn’t in question. Infinity exists, the infinitesimal does not.

x=.9999…

10x=9.9999…

Subtract x from both sides

9x=9

x=1

There it is, folks.

Two candidates that support genocide, but one is a christofascist. No matter who you vote for, genocide support wins. But you think it’s better to give the christofascist better odds than to inconvenience yourself with a vote you don’t 100% agree with, and possibly abstain from your chance to ever vote again. Not voting won’t fix the issue, since there’s no threshold on voter turnout for the election to count. The struggle against genocide must be fought in other ways. So unfortunately, this fall you’re getting genocide, so please make sure you don’t get fascism too.

Except, it’s not an attempt to end democracy, as fascism is.

You just have to appreciate the craftsmanship of a good, clever, witty insult. Can’t really get mad!