- #1
- 858
- 914
The concept's main theorem goes as follows:
Suppose that [itex]w = F(x,y) [/itex] satisfies the following criteria at point A = (a,b).
[tex]\begin{cases}\exists\delta > 0\colon F\ is\ continuous \forall (x,y)\in B(A,\delta)\\
\exists \frac{\partial}{\partial y}F , continuous \\
F(A) = 0, F_y \neq 0\end{cases} \Rightarrow \exists y = f(x) continous[/tex]
The absolute correct definition is an utter pain to get written down, though that's not my purpose. This is enough information to be able to recognize what I am getting at. We call these things "undeveloped" or "inexplicit" functions, but I can't find anything with those keywords so it's (again) my apparent lack of vocabulary that's at work here :<
Suppose that [itex]w = F(x,y) [/itex] satisfies the following criteria at point A = (a,b).
[tex]\begin{cases}\exists\delta > 0\colon F\ is\ continuous \forall (x,y)\in B(A,\delta)\\
\exists \frac{\partial}{\partial y}F , continuous \\
F(A) = 0, F_y \neq 0\end{cases} \Rightarrow \exists y = f(x) continous[/tex]
The absolute correct definition is an utter pain to get written down, though that's not my purpose. This is enough information to be able to recognize what I am getting at. We call these things "undeveloped" or "inexplicit" functions, but I can't find anything with those keywords so it's (again) my apparent lack of vocabulary that's at work here :<