# [SOLVED]pointwise convergence

#### Fermat

##### Active member
Does pointwise convergence mean that |$f_{n}$-$f$|->0 for each x?

#### Opalg

##### MHB Oldtimer
Staff member
Does pointwise convergence mean that |$f_{n}$-$f$|->0 for each x?
Yes. More precisely, it means that for each $x$ (in some specified domain) $|f_n(x) - f(x)| \to0$ as $n\to\infty$.

#### chisigma

##### Well-known member
Does pointwise convergence mean that |$f_{n}$-$f$|->0 for each x?
Wellcome back to MHB Fermat!... yes, pointwise convergence to f(x) means that $\lim_{n \rightarrow \infty} |f_{n} (x) - f(x)| = 0$ for any x in the domain...

Kind regards

$\chi$ $\sigma$