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growing_sequence [2013/08/09 16:02] nikolaj |
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 ==== | ||
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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: $A_n\uparrow \hat A \equiv A\in \mathrm{GrowingSequence}(X)\ \land\ \lim_{n\to\infty}A_n=\hat A$ | |
- | ==== Context ==== | + | ==== Parents ==== |
=== Subset of === | === Subset of === | ||
- | [[Sequence]] | + | [[Infinite sequence]] |