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falling_sequence [2013/09/08 15:41] nikolaj |
falling_sequence [2013/09/08 15:43] nikolaj |
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| For [[Growing sequence|growing sequences]] we have: $\lim_{n\to\infty}A_n=\bigcup_{n=1}^\infty A_n$. | For [[Growing sequence|growing sequences]] we have: $\lim_{n\to\infty}A_n=\bigcup_{n=1}^\infty A_n$. | ||
| === Predicates === | === Predicates === | ||
| - | | @#FFBB00: $A_n\downarrow \hat A \equiv (A\in \mathrm{FallingSequence}(X))\land(\lim_{n\to\infty}A_n=\hat A)$ | | + | | @#EEEE55: $A_n\downarrow \hat A \equiv A\in \mathrm{FallingSequence}(X)\ \land\ \lim_{n\to\infty}A_n=\hat A$ | |
| ==== Parents ==== | ==== Parents ==== | ||
| === Subset of === | === Subset of === | ||
| [[Infinite sequence]] | [[Infinite sequence]] | ||
