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ε-δ_function_limit [2014/03/11 09:31] nikolaj |
ε-δ_function_limit [2014/03/21 11:11] 127.0.0.1 external edit |
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| ===== ε-δ function limit ===== | ===== ε-δ function limit ===== | ||
| ==== Set ==== | ==== Set ==== | ||
| - | | @#88DDEE: $\langle X,d_X\rangle$ ... metric space | | + | | @#55CCEE: context | @#55CCEE: $\langle X,d_X\rangle$ ... metric space | |
| - | | @#88DDEE: $\langle Y,d_Y\rangle$ ... metric space | | + | | @#55CCEE: context | @#55CCEE: $\langle Y,d_Y\rangle$ ... metric space | |
| - | | @#88DDEE: $f:X\to Y$ | | + | | @#55CCEE: context | @#55CCEE: $f:X\to Y$ | |
| - | | @#88DDEE: $\xi\in X$ | | + | | @#55CCEE: context | @#55CCEE: $\xi\in X$ | |
| - | | @#FFBB00: $\mathrm{lim}_{x\to \xi}\ f(x)\equiv y_\xi$ | | + | | @#FFBB00: definiendum | @#FFBB00: $\mathrm{lim}_{x\to \xi}\ f(x)\equiv y_\xi$ | |
| - | | @#DDDDDD: $\varepsilon,\delta\in \mathbb R_+^*$ | | + | | @#DDDDDD: range | @#DDDDDD: $\varepsilon,\delta\in \mathbb R_+^*$ | |
| - | | @#55EE55: $\forall\varepsilon.\ \exists \delta.\ \forall x.\ [\ 0<d_X(x,\xi)<\delta\ ] \Rightarrow [\ d_Y(f(x),y_\xi)<\varepsilon\ ]$ | | + | | @#55EE55: postulate | @#55EE55: $\forall\varepsilon.\ \exists \delta.\ \forall x.\ [\ 0<d_X(x,\xi)<\delta\ ] \Rightarrow [\ d_Y(f(x),y_\xi)<\varepsilon\ ]$ | |
| ==== Discussion ==== | ==== Discussion ==== | ||
