Differences

This shows you the differences between two versions of the page.

 growing_sequence [2013/09/08 15:42]nikolaj growing_sequence [2014/03/21 11:11] Line 1: Line 1: - ===== Growing sequence ===== - ==== Definition ==== - | @#88DDEE: $X$ | - | @#FFBB00: $A\in \mathrm{GrowingSequence}(X)$ | - - | @#55EE55: $A\in \mathrm{InfSequence}(X)$ | - - | $n\in \mathbb N$ | - - | @#55EE55: $A_{n}\subseteq A_{n+1}$ | - - ==== Discussion ==== - - === Ramifications === - For [[Falling sequence|falling sequences]] we have: $\lim_{n\to\infty}A_n=\bigcap_{n=1}^\infty A_n$. - - For growing sequences we have: $\lim_{n\to\infty}A_n=\bigcup_{n=1}^\infty A_n$. - === Predicates === - | @#FFBB00: $A_n\uparrow \hat A \equiv (A\in \mathrm{GrowingSequence}(X))\land(\lim_{n\to\infty}A_n=\hat A)$ | - ==== Parents ==== - === Subset of === - [[Infinite sequence]]