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(1 + (-1)) + (2 + (-2)) + (3 + (-3)) +... = 0 + 0 + 0 + ... = 0
Zero cannot represent both nothing and everything in the same mathematical system of values, and as long as we remember that, we can discover a second mathematical system, very similar to ordinary math, and yet very different, because in this new system, zero represents a mathematical everything, which produces a whole other kind of math. And what is perhaps most interesting, is that in the same way that there isn't a number in ordinary math to represent everything, in this new system there isn't a number to represent nothing.