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| Both sides previous revision Previous revision Next revision | Previous revision | ||
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growing_sequence [2013/09/08 15:40] nikolaj |
growing_sequence [2013/09/08 15:43] nikolaj |
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| | @#88DDEE: $X$ | | | @#88DDEE: $X$ | | ||
| - | | @#55EE55: $A\in \mathrm{GrowingSequence}(X) $ | | + | | @#FFBB00: $A\in \mathrm{GrowingSequence}(X) $ | |
| - | | @#55EE55: $A\in \mathrm{Sequence}(X) $ | | + | | @#55EE55: $A\in \mathrm{InfSequence}(X) $ | |
| | $n\in \mathbb N$ | | | $n\in \mathbb N$ | | ||
| Line 18: | Line 18: | ||
| For growing sequences we have: $\lim_{n\to\infty}A_n=\bigcup_{n=1}^\infty A_n$. | For growing sequences we have: $\lim_{n\to\infty}A_n=\bigcup_{n=1}^\infty A_n$. | ||
| === Predicates === | === Predicates === | ||
| - | | @#FFBB00: $A_n\uparrow \hat A \equiv (A\in \mathrm{GrowingSequence}(X))\land(\lim_{n\to\infty}A_n=\hat A)$ | | + | | @#EEEE55: $A_n\uparrow \hat A \equiv A\in \mathrm{GrowingSequence}(X)\ \land\ \lim_{n\to\infty}A_n=\hat A$ | |
| ==== Parents ==== | ==== Parents ==== | ||
| === Subset of === | === Subset of === | ||
| [[Infinite sequence]] | [[Infinite sequence]] | ||
