## ε-δ function limit

### Set

todo:
Rather define the set of all sequences which have a limit in the below sense
this is the domain of “lim” though of as function (on all sequences it would be a partial function)
 context $\langle X,d_X\rangle$ … metric space context $\langle Y,d_Y\rangle$ … metric space context $f:X\to Y$ context $\xi\in X$
 definiendum $\mathrm{lim}_{x\to \xi}\ f(x)\equiv y_\xi$
 range $\varepsilon,\delta\in \mathbb R_+^*$
 postulate \$\forall\varepsilon.\ \exists \delta.\ \forall x.\ [\ 0