File:Pm1234 linearity.svg

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Summary

DescriptionPm1234 linearity.svg	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.
Date	5 March 2007
Source	Own work
Author	User:Melchoir
Other versions	PNG version

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	This licensing tag was added to this file as part of the GFDL licensing update.CC BY-SA 3.0truetrue

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File history

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	Date/Time	Dimensions	User	Comment
current	12:16, 1 January 2008	432 × 282 (7 KB)	Papa November	Trimmed useless Adobe Illustrator metadata. This may have been causing the display errors. No copyright claimed on non-creative derivative work
	05:22, 5 March 2007	432 × 282 (29 KB)	Melchoir	alter slightly
	04:03, 5 March 2007	432 × 282 (29 KB)	Melchoir	Adding 4 copies of 1 − 2 + 3 − 4 + · · ·, using only shifts and term-by-term addition, yields 1.