# Differences

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 falling_sequence [2013/09/08 15:43]nikolaj falling_sequence [2014/03/21 11:11] (current) Both sides previous revision Previous revision 2013/09/08 15:43 nikolaj 2013/09/08 15:41 nikolaj 2013/09/08 15:37 nikolaj 2013/09/08 15:37 nikolaj 2013/09/06 22:04 external edit2013/08/09 16:02 nikolaj 2013/08/09 16:01 nikolaj 2013/08/09 15:59 nikolaj 2013/08/09 15:49 nikolaj 2013/08/09 15:43 nikolaj created 2013/09/08 15:43 nikolaj 2013/09/08 15:41 nikolaj 2013/09/08 15:37 nikolaj 2013/09/08 15:37 nikolaj 2013/09/06 22:04 external edit2013/08/09 16:02 nikolaj 2013/08/09 16:01 nikolaj 2013/08/09 15:59 nikolaj 2013/08/09 15:49 nikolaj 2013/08/09 15:43 nikolaj created 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: $A\in \mathrm{FallingSequence}(X)$ | - | @#55EE55: $A\in \mathrm{InfSequence}(X)$ | + | @#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 === - | @#EEEE55: $A_n\downarrow \hat A \equiv A\in \mathrm{FallingSequence}(X)\ \land\ \lim_{n\to\infty}A_n=\hat A$ | + | @#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]]