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falling_sequence [2013/09/08 15:41]
nikolaj
falling_sequence [2014/03/21 11:11]
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-===== Falling sequence ===== 
-==== Definition ==== 
-| @#88DDEE: $X$ |  
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-| @#FFBB00: $A\in \mathrm{FallingSequence}(X) $ | 
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-| @#55EE55: $A\in \mathrm{InfSequence}(X) $ | 
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-| $n\in \mathbb N$ | 
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-| @#55EE55: $A_{n+1}\subseteq A_n $ | 
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-==== Discussion ==== 
- 
-=== Ramifications === 
-For falling sequences we have: $\lim_{n\to\infty}A_n=\bigcap_{n=1}^\infty A_n$. 
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-For [[Growing sequence|growing sequences]] we have: $\lim_{n\to\infty}A_n=\bigcup_{n=1}^\infty A_n$. 
-=== Predicates === 
-| @#FFBB00: $A_n\downarrow \hat A \equiv (A\in \mathrm{FallingSequence}(X))\land(\lim_{n\to\infty}A_n=\hat A)$ | 
-==== Parents ==== 
-=== Subset of === 
-[[Infinite sequence]] 
  
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