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I'm a high school student. My peer and I have done some work on the Ballot Theorem counting problem and Catalan Numbers. We have come up with a new proof to the Ballot Theorem and we demonstrate the ...

From $0 = 0.5 - 0.5 = 0.5 - \sqrt{0.25}$, we can adjust the subtrahend slightly to obtain $$0.5 - \sqrt{0.249} = 0.001\ 001\ 002\ 005\ 014\ 042\ldots$$ where the decimal representation contains the ...