Hello.(adsbygoogle = window.adsbygoogle || []).push({});

I know this:

If (a_n) is a bounded below decreasing sequence, then

lim (a_n) = inf { a_n / n = 1,... }

n->oo

How to translate this to real functions ?

I mean, I have read that:

lim (sup { f(x) / 0< |x-a|< e}) =

e->0

inf { sup {f(x) / 0< |x-a|< e} / e > 0}

and i suppose it has something to do with the previous but I fail to see how.

Can you help me?

**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!

# From decreasing sequences to decreasing functions

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