===== 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)

| @#55CCEE: context     | @#55CCEE: $\langle X,d_X\rangle$ ... metric space |
| @#55CCEE: context     | @#55CCEE: $\langle Y,d_Y\rangle$ ... metric space |
| @#55CCEE: context     | @#55CCEE: $f:X\to Y$ | 
| @#55CCEE: context     | @#55CCEE: $\xi\in X$ |

| @#FFBB00: definiendum | @#FFBB00: $\mathrm{lim}_{x\to \xi}\ f(x)\equiv y_\xi$ |

| @#DDDDDD: range       | @#DDDDDD: $\varepsilon,\delta\in \mathbb R_+^*$ |

| @#55EE55: postulate   | @#55EE55: $\forall\varepsilon.\ \exists \delta.\ \forall x.\ [\ 0<d_X(x,\xi)<\delta\ ] \Rightarrow [\ d_Y(f(x),y_\xi)<\varepsilon\ ]$ | 

==== Discussion ====
==== Parents ====
=== Context ===
[[Metric space]]