Category:Limits of Sets

From ProofWiki
Jump to navigation Jump to search

This category contains results about Limits of Sets.

Let $\Bbb S = \set {E_n : n \in \N}$ be a sequence of sets.

Let the limit superior of $\Bbb S$ be equal to the limit inferior of $\Bbb S$.

Then the limit of $\Bbb S$, denoted $\ds \lim_{n \mathop \to \infty} E_n$, is defined as:

$\ds \lim_{n \mathop \to \infty} E_n := \limsup_{n \mathop \to \infty} E_n$

and so also:

$\ds \lim_{n \mathop \to \infty} E_n := \liminf_{n \mathop \to \infty} E_n$

and $\Bbb S$ converges to the limit.


This category has the following 2 subcategories, out of 2 total.

Pages in category "Limits of Sets"

The following 3 pages are in this category, out of 3 total.