Category:Inequality Rule for Real Sequences

From ProofWiki
Jump to navigation Jump to search

This category contains pages concerning Inequality Rule for Real Sequences:

Let $\sequence {x_n}$ and $\sequence {y_n}$ be sequences in $\R$.

Let $\sequence {x_n}$ and $\sequence {y_n}$ be convergent to the following limits:

$\ds \lim_{n \mathop \to \infty} x_n = l$
$\ds \lim_{n \mathop \to \infty} y_n = m$

Let there exist $N \in \N$ such that:

$\forall n \ge N: x_n \le y_n$


$l \le m$