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i agree with you. if u are taking Z as 1-1+1-1+1..., you cannot assume that Z and Z is also 1-1+1-1+1..... Z could either end with a +1 or a - 1, thus, if it ends with a +1 Z and Z gives 1-1+1-1+1-1+1........1-1+1+1-1+1-1....... you would get a 1+1+1 in the section between the first Z and the second Z. which means Z+Z≠Z and so the infinite sequence correct and equals to half.

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