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growing_sequence [2013/09/06 22:04] 127.0.0.1 external edit |
growing_sequence [2014/03/21 11:11] (current) |
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| ===== Growing sequence ===== | ===== Growing sequence ===== | ||
| - | ==== Definition ==== | + | ==== Set ==== |
| - | | @#88DDEE: $X$ | | + | | @#55CCEE: context | @#55CCEE: $X$ | |
| - | | @#55EE55: $A\in \mathrm{GrowingSequence}(X) $ | | + | | @#FFBB00: definiendum | @#FFBB00: $A\in \mathrm{GrowingSequence}(X) $ | |
| + | |||
| + | | @#55EE55: postulate | @#55EE55: $A\in \mathrm{InfSequence}(X) $ | | ||
| - | | @#88DDEE: $A\in \mathrm{Sequence}(X) $ | | ||
| | $n\in \mathbb N$ | | | $n\in \mathbb N$ | | ||
| - | | @#55EE55: $A_{n}\subseteq A_{n+1} $ | | + | | @#55EE55: postulate | @#55EE55: $A_{n}\subseteq A_{n+1} $ | |
| ==== Discussion ==== | ==== Discussion ==== | ||
| Line 17: | 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: predicate | @#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 === | ||
| - | [[Sequence]] | + | [[Infinite sequence]] |
