My question involves supremums and their implications:(adsbygoogle = window.adsbygoogle || []).push({});

say I have the sequences [itex]\left\{x_{k}\right\}_{k=1}^{\infty}[/itex] and [itex]\left\{y_{k}\right\}_{k=1}^{\infty}[/itex]

and I know [itex]sup \left\{x_{k}:k\in N \right\} \leq sup \left\{y_{k}:k\in N \right\} [/itex]

What can I say about the sequence [itex]\left\{x_{k}\right\}_{k=1}^{\infty}[/itex]?

Can anyone suggest a text or website that goes into detail about supremums and how to use them? All my Analysis books just announce the definition of a supremum and move on, but I'd like to see a little more exposition, especially with what can be done with two sets correlated by their sups or infs as above.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Set of sequences, supremum

**Physics Forums | Science Articles, Homework Help, Discussion**