# 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:

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

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

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

Then:

- $l \le m$

## Pages in category "Inequality Rule for Real Sequences"

The following 7 pages are in this category, out of 7 total.