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Let $\{ a_j \}_{j \in \mathbb{N}}$ be any sequence of real numbers satisfying the following property:

There exists a number $N \in \mathbb{N}$ such that $a_k<a_j$ for all $k\geq j+N$.

What is such a sequence called?

If $N=1$, $\{a_j\}_{j \in \mathbb{N}}$ is of course an decreasing sequence.

One example of such a sequence with N=2 is -1,0,-2,-1,-3,-2,-4,-3,...

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Isn't it decreasing if $N=1$? You have $k\gt j$ implies $a_k\lt a_j$. –  Gerry Myerson Jan 21 '13 at 12:07
    
Typo :) It should now be correct –  malin Jan 21 '13 at 19:19

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