===== Growing sequence =====
==== Set ====
| @#55CCEE: context     | @#55CCEE: $X$ | 

| @#FFBB00: definiendum | @#FFBB00: $A\in \mathrm{GrowingSequence}(X) $ |

| @#55EE55: postulate   | @#55EE55: $A\in \mathrm{InfSequence}(X) $ |

| $n\in \mathbb N$ |

| @#55EE55: postulate   | @#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 ===
| @#EEEE55: predicate   | @#EEEE55: $A_n\uparrow \hat A \equiv A\in \mathrm{GrowingSequence}(X)\ \land\ \lim_{n\to\infty}A_n=\hat A$ |
==== Parents ====
=== Subset of ===
[[Infinite sequence]]