\begin{definition}[Definition:Conjugate Point (Calculus of Variations)/Definition 3]
Let $y = \map y x$ and $y = \map {\tilde y} x$ be extremal functions.
Let:
:$M = \paren {a, \map y a}$
:$\tilde M = \paren {\tilde a, \map y {\tilde a} }$
Let both $y = \map y x$ and $y = \map {\tilde y} x$ pass through the point $M$.
Let 
:$\ds \lim_{\norm {\map y x - \map {\tilde y} x}_{1, \infty} \to 0} \sqbrk {\paren {x, \map y x}: \map y x - \map {\tilde y} x = 0} = \tilde M$
In other words, let $\tilde M$ be the limit points of intersection of $y = \map y x$ and $y = \map {\tilde y} x$ as $\norm {\map y x - \map {\tilde y} x}_{1, \infty} \to 0$.
{{explain|the notation $\norm {\map y x - \map {\tilde y} x}_{1, \infty}$ with particular regard to the subscript
This is most likely the standard norm of Sobolev space, also know as np-norm. Original source never calls it by word; only by special symbols}}
Then $\tilde M$ is '''conjugate''' to $M$.
\end{definition}