Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision Next revision | Previous revision | ||
|
falling_sequence [2013/09/08 15:37] nikolaj |
falling_sequence [2014/03/21 11:11] (current) |
||
|---|---|---|---|
| Line 1: | Line 1: | ||
| ===== Falling sequence ===== | ===== Falling sequence ===== | ||
| - | ==== Definition ==== | + | ==== Set ==== |
| - | | @#88DDEE: $X$ | | + | | @#55CCEE: context | @#55CCEE: $X$ | |
| - | | @#FFBB00: $A\in \mathrm{FallingSequence}(X) $ | | + | | @#FFBB00: definiendum | @#FFBB00: $A\in \mathrm{FallingSequence}(X) $ | |
| - | | @#88DDEE: $A\in \mathrm{InfSequence}(X) $ | | + | | @#55EE55: postulate | @#55EE55: $A\in \mathrm{InfSequence}(X) $ | |
| | $n\in \mathbb N$ | | | $n\in \mathbb N$ | | ||
| - | | @#55EE55: $A_{n+1}\subseteq A_n $ | | + | | @#55EE55: postulate | @#55EE55: $A_{n+1}\subseteq A_n $ | |
| ==== Discussion ==== | ==== Discussion ==== | ||
| Line 18: | Line 18: | ||
| 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: predicate | @#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]] | ||
