I strongly predict that if you make your argument really precise (as you did in the main post), it will have a visible flaw in it. In particular, I expect the fact that r and r-1000 are indistinguishable to prevent the argument from going through (though it’s hard to say exactly how this applies without having access to a sufficiently mathematical argument).

I strongly predict that if you make your argument really precise (as you did in the main post), it will have a visible flaw in it. In particular, I expect the fact that r and r-1000 are indistinguishable to prevent the argument from going through (though it’s hard to say exactly how this applies without having access to a sufficiently mathematical argument).