Limit of sequence of functions

1. Jul 31, 2011

math771

Hi. When we say that $\displaystyle \lim_{n \to \infty}f_n(x)=g(x)$, do we mean that $f_n$ is pointwise or uniformly convergent to $g$?
Thanks.

2. Aug 1, 2011

SteveL27

The convention is that pointwise is assumed unless you specifically say it's uniform.

3. Aug 1, 2011

I like Serena

The x is unspecified, meaning your statement is incomplete.
Usually it is implied that you mean "for each x in the applicable domain of the functions".
This also means that you imply "pointwise convergent".

If you left out x completely by saying $\displaystyle \lim_{n \to \infty}f_n=g$, you would specify "uniform convergent".

4. Aug 1, 2011

math771

Thanks, both of you.