If you're given a sequence [itex]\{x_n\}[/itex], do you have(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\sup_n x_n = \lim_{n\to \infty} \left( \max\limits_{1 \leq k \leq n} x_k \right)

[/tex]

I've never seen this definition before, but it makes sense.

...and if it's NOT the same as the supremum...what *is* it?

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# Definition of supremum

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