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File:Pm1234 linearity.svg

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Summary

Description
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
Source Own work
Author User:Melchoir
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This licensing tag was added to this file as part of the GFDL licensing update.
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attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 2.5 Generic, 2.0 Generic and 1.0 Generic license.
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
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inception

5 March 2007

File history

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Date/TimeThumbnailDimensionsUserComment
current12:16, 1 January 2008Thumbnail for version as of 12:16, 1 January 2008432 × 282 (7 KB)Papa NovemberTrimmed useless Adobe Illustrator metadata. This may have been causing the display errors. No copyright claimed on non-creative derivative work
05:22, 5 March 2007Thumbnail for version as of 05:22, 5 March 2007432 × 282 (29 KB)Melchoiralter slightly
04:03, 5 March 2007Thumbnail for version as of 04:03, 5 March 2007432 × 282 (29 KB)MelchoirAdding 4 copies of 1 − 2 + 3 − 4 + · · ·, using only shifts and term-by-term addition, yields 1.

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