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finite_sequence [2013/09/16 21:36] nikolaj |
finite_sequence [2014/03/21 11:11] 127.0.0.1 external edit |
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| ===== Finite sequence ===== | ===== Finite sequence ===== | ||
| - | ==== Definition ==== | + | ==== Set ==== |
| - | | @#88DDEE: $X$ | | + | | @#55CCEE: context | @#55CCEE: $X$ | |
| - | | @#FFBB00: $ A\in \text{FinSequence}(X) $ | | + | | @#FFBB00: definiendum | @#FFBB00: $ A\in \text{FinSequence}(X) $ | |
| - | | @#DDDDDD: $ n\in \mathbb N $ | | + | | @#DDDDDD: range | @#DDDDDD: $ n\in \mathbb N $ | |
| - | | @#55EE55: $\exists n.\ A: \mathrm{range}(n)\to X$ | | + | | @#55EE55: postulate | @#55EE55: $\exists n.\ A: \mathrm{range}(n)\to X$ | |
| ==== Discussion ==== | ==== Discussion ==== | ||
| - | |||
| - | == Multi-index notation == | ||
| - | |||
| - | Let $\alpha \in \mathrm{FinSequence}(\mathbb N)$, then | ||
| - | |||
| - | * $|\alpha| = \sum_i \alpha_i $ | ||
| - | |||
| - | * $x^\alpha = \prod_i x_i^{\alpha_i}$ | ||
| - | |||
| - | * $f^{(\alpha)}(x) = \prod_i \frac{\partial^{\alpha_i}}{\partial x_i^{\alpha_i}} f(x)$ | ||
| === Reference === | === Reference === | ||
| ==== Parents ==== | ==== Parents ==== | ||
| - | === Context === | + | === Related === |
| [[Natural number range]] | [[Natural number range]] | ||
