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ε-δ function limit
Set
| 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 | $\forall\varepsilon.\ \exists \delta.\ \forall x.\ [\ 0<d_X(x,\xi)<\delta\ ] \Rightarrow [\ d_Y(f(x),y_\xi)<\varepsilon\ ]$ |
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