File:Pm1234 linearity.png
Original file (1,728 × 1,128 pixels, file size: 85 KB, MIME type: image/png)
Captions
File:Pm1234 linearity.svg is a vector version of this file. It should be used in place of this PNG file when not inferior.
File:Pm1234 linearity.png → File:Pm1234 linearity.svg
For more information, see Help:SVG.
|
Summary
editAdding 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.
Licensing
editPermission 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.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license. | ||
| ||
This licensing tag was added to this file as part of the GFDL licensing update.http://creativecommons.org/licenses/by-sa/3.0/CC BY-SA 3.0Creative Commons Attribution-Share Alike 3.0truetrue |
- 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.
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 17:29, 13 March 2007 | 1,728 × 1,128 (85 KB) | Melchoir (talk | contribs) | {{vector version available|Pm1234 linearity.svg}} == Summary == 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. |
You cannot overwrite this file.
File usage on Commons
There are no pages that use this file.
File usage on other wikis
The following other wikis use this file:
- Usage on ca.wikipedia.org
- Usage on es.wikipedia.org
- Usage on fr.wikipedia.org
- Usage on gl.wikipedia.org
- Usage on ja.wikipedia.org
- Usage on no.wikipedia.org
- Usage on sl.wikipedia.org
- Usage on th.wikipedia.org