Sanakirja
Tekoälykääntäjä
| Kieli | Käännökset |
|---|---|
| italia | numero p-adico |
Määritelmät
Substantiivi
- (number theory) An element of a completion of the field of rational numbers with respect to a ''p''-adic ultrametric.
Esimerkit
- The expansion (21)2121p is equal to the rational p-adic number {2 p + 1 \over p^2 - 1}.
- In the set of 3-adic numbers, the closed ball of radius 1/3 "centered" at 1, call it B, is the set \{x | ∃ n ∈ \mathbb{Z} . \, x = 3 n + 1 \} . This closed ball partitions into exactly three smaller closed balls of radius 1/9: \{x | ∃ n ∈ \mathbb{Z} . \, x = 1 + 9 n \} , \{x | ∃ n ∈ \mathbb{Z} . \, x = 4 + 9 n \}, and \{x | ∃ n ∈ \mathbb{Z} . \, x = 7 + 9 n \} . Then each of those balls partitions into exactly 3 smaller closed balls of radius 1/27, and the sub-partitioning can be continued indefinitely, in a fractal manner. Likewise, going upwards in the hierarchy, B is part of the closed ball of radius 1 centered at 1, namely, the set of integers. Two other closed balls of radius 1 are "centered" at 1/3 and 2/3, and all three closed balls of radius 1 form a closed ball of radius 3, \{x| ∃ n ∈ \mathbb{Z} . \, x = 1 + {n\over 3} \} , which is one out of three closed balls forming a closed ball of radius 9, and so on.
Taivutusmuodot
| Monikko | p-adic numbers |
Luokat
(number theory) An element of a completion of the field of rational numbers with respect to a ''p''-adic ultrametric.
The 3-adic integers, with selected corresponding characters on their Pontryagin dual group
(number theory) An element of a completion of the field of rational numbers with respect to a ''p''-adic ultrametric.
Visual depiction of the 3-adic integers as a metric space