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KnifeMissile - I'm a little bit confused. You'll have to fogive me, as my infinite sum theory is a bit rusty.
First of all, what do you mean by "just over x." If it's a distinct number from x, then there are an infinite number of real numbers between it and x, so really any number greater than x would do. If it's not a distinct number from x, then it is x, and so you're just adding and subtracting 0 over and over, in which case the only number you can form is x by rearranging.
Also, I do recall that there are infinite sums that do not converge to a number, but also do not diverge to infinity. Think about this one: 2 - 2 + 2 - 2 + 2 - 2 + ... At any one point it's either 2 or 0, but I certaintly wouldn't say it converges to 1.
Could you try and clarify your proof a bit? Maybe write out some equations and examples?
I'm also a bit curious about WHAT you're trying to prove. I had to read to the end just to find any kind of conclusion... if you clearly stated what you were trying to prove at the beginning, it would make reading it much easier.
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