Difference between revisions of "Multiple sequence"
From Encyclopedia of Mathematics
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| − | '' | + | ''$k$-tuple sequence, of elements of a given set $X$'' |
| − | A mapping of the | + | A mapping of the $k$-th power $\mathbb{N}^k$ of the set of natural numbers $\mathbb{N}$ into the set $X$. An element (or term) of a multiple sequence $f : \mathbb{N}^k \rightarrow X$ is an ordered set of $k+1$ elements $(n_1,\ldots,n_k,x)$, where $x = f(n_1,\ldots,n_k)$, $x \in X$, $(n_1,\ldots,n_k) \in \mathbb{N}^k$, i.e. $n_j \in \mathbb{N}$ ($j = 1,\ldots,k$). The element is also denoted by $x_{n_1 \ldots n_k}$. |
Latest revision as of 18:52, 12 October 2014
$k$-tuple sequence, of elements of a given set $X$
A mapping of the $k$-th power $\mathbb{N}^k$ of the set of natural numbers $\mathbb{N}$ into the set $X$. An element (or term) of a multiple sequence $f : \mathbb{N}^k \rightarrow X$ is an ordered set of $k+1$ elements $(n_1,\ldots,n_k,x)$, where $x = f(n_1,\ldots,n_k)$, $x \in X$, $(n_1,\ldots,n_k) \in \mathbb{N}^k$, i.e. $n_j \in \mathbb{N}$ ($j = 1,\ldots,k$). The element is also denoted by $x_{n_1 \ldots n_k}$.
How to Cite This Entry:
Multiple sequence. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Multiple_sequence&oldid=11606
Multiple sequence. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Multiple_sequence&oldid=11606
This article was adapted from an original article by L.D. Kudryavtsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article