File:Pm1234 linearity.svg

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Pm1234_linearity.svg‎ (SVG file, nominally 432 × 282 pixels, file size: 7 KB)

[edit] Summary

Description	Pm1234 linearity.svg English: 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(2007-03-05)
Source	Self-made by user
Author	User:Melchoir
Permission (Reusing this image)	See below.
Other versions	PNG version

[edit] Licensing

I, the copyright holder of this work, hereby publish it under the following licenses:

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled "GNU Free Documentation License".

This file is licensed under the Creative Commons Attribution ShareAlike 3.0 License. In short: you are free to share and make derivative works of the file under the conditions that you appropriately attribute it, and that you distribute it only under a license identical to this one. Official license

This licensing tag was added to this file as part of the GFDL licensing update.

This file is licensed under the Creative Commons Attribution ShareAlike 2.5, Attribution ShareAlike 2.0 and Attribution ShareAlike 1.0 License. In short: you are free to share and make derivative works of the file under the conditions that you appropriately attribute it, and that you distribute it only under a license identical to this one.

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File history

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	Date/Time	Thumbnail	Dimensions	User	Comment
current	12:16, 1 January 2008		432×282 (7 KB)	Papa November (Talk \| contribs)	(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 (Talk \| contribs)	(alter slightly)
	04:03, 5 March 2007		432×282 (29 KB)	Melchoir (Talk \| contribs)	(Adding 4 copies of 1 − 2 + 3 − 4 + · · ·, using only shifts and term-by-term addition, yields 1.)