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Growing sequence
Definition
| $X$ |
| $A\in \mathrm{GrowingSequence}(X) $ |
| $A\in \mathrm{Sequence}(X) $ |
| $n\in \mathbb N$ |
| $A_{n}\subseteq A_{n+1} $ |
Discussion
Ramifications
For 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
| $A_n\uparrow \hat A \equiv (A\in \mathrm{GrowingSequence}(X))\land(\lim_{n\to\infty}A_n=\hat A)$ |
Parents
Subset of
