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.

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Name one thing he did that was worse than what the republicans have done? Voting for Biden this fall doesn't means you have to agree with him. You simply have to agree that having Trump win would be worse. This is like the trolley problem - you're fucked either way but you can decide how fucked you prefer being.

Yes he is a conservative and will crush all attempts to end capitalism, but you have to admit one party is clearly more zealous about ending democracy than the other.

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So when the republican christofascist dictatorship comes, at least you will have a clean conscience, knowing you didn't vote for preserving satus quo, shitty as it may be. Good for you!

I hope, if you can't find it in yourself to put a ballot in the urn for the lesser evil, that you can put a bullet in the head of the greater.

You have given Dobby clothes. Dobby is free!