File:Pm1234 linearity.png

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Adding 4 copies of 1 − 2 + 3 − 4 + · · ·, using only shifts and term-by-term addition, yields 1.

Only the first four terms of the series are shown. A white disk represents +1; a reddish disk represents −1. The units are grouped on top of each other as they occur within the terms of the series. A black line indicates a plus/minus pair, which annihilate to 0. An intermediate reduction to two copies of 1 − 1 + 1 − 1 + · · · is visible in the top row. The result of the addition is a single positive unit, highlighted in green at the upper left.

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