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Description |
English: 1 − 2 + 3 − 4 + · · · as the Cauchy product of two copies of 1 − 1 + 1 − 1 + · · ·.
The illustration uses the rectangle metaphor for multiplication. One copy of 1 − 1 + 1 − 1 + · · · is depicted at the top, another at the left. A black length or area represents a positive quantity; a red length or area represents a negative quantity. Multiplying two line segments results in a rectangle whose color is determined by the law for multiplying signed numbers:
- 1 * 1 = 1
- −1 * 1 = −1
- 1 * −1 = −1
- −1 * −1 = 1
The double series resulting from the multiplication of the two single series is expressed as a single series using the Cauchy product rule. Each term of the resulting series is a combination of terms from the double series running from south-west to north-east. The result is identified as 1 − 2 + 3 − 4 + · · ·.
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Source |
User created
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Date |
2007-03-04
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Author |
user:Melchoir
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| Date et heure | Dimensions | Utilisateur | Commentaire |
actuel | 14 avril 2007 à 14:14 | 570×570 (27 Kio) | Ysangkok | |
| 4 mars 2007 à 05:55 | 570×570 (41 Kio) | Melchoir | |
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