Category:Inequality Rule for Real Sequences

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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:

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

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

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


$l \le m$