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infinite_sequence [2013/09/08 15:33] nikolaj |
infinite_sequence [2014/03/21 11:11] (current) |
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| ===== Infinite sequence ===== | ===== Infinite sequence ===== | ||
| - | ==== Definition ==== | + | ==== Set ==== |
| - | | @#88DDEE: $X$ | | + | | @#55CCEE: context | @#55CCEE: $X$ | |
| - | | | + | |
| - | | @#FFBB00: $ A\in \mathrm{InfSequence}(X) $ | | + | |
| - | | @#55EE55: $A: \mathbb N\to X$ | | + | | @#FFBB00: definiendum | @#FFBB00: $ A\in \mathrm{InfSequence}(X) $ | |
| + | |||
| + | | @#55EE55: postulate | @#55EE55: $A: \mathbb N\to X$ | | ||
| ==== Discussion ==== | ==== Discussion ==== | ||
| - | Instead of $\langle n,A(n)\rangle$, we also write $A_n$ and denote the whole sequence by $(A_n)_{n\mathbb N}$. | + | Instead of $\langle n,A(n)\rangle$, we also write $A_n$ and denote the whole sequence by $(A_n)_{n\in\mathbb N}$ or just $(A_n)$. |
| ==== Parents ==== | ==== Parents ==== | ||
| === Subset of === | === Subset of === | ||
| [[Function]] | [[Function]] | ||
| - | === Context === | + | === Related === |
| [[Natural number]] | [[Natural number]] | ||
