necessary to understand how the concepts of *eventually in* and *frequently in* of Appendix A2 apply in examples (a) and (b) of Fig. [\[Fig: Example2\_1\].]{} In these two examples we have two subsequences one each for the even indices and the other for the odd. For a point-to-point functional relation, this would mean that the sequence frequents the adherence set $\textrm{adh}(x)$ of the sequence $(x_{n})$ but does not converge anywhere as it is not eventually in every neighbourhood of any point. For a multifunctional limit however it is possible, as demonstrated by these examples, for the subsequences to be eventually in every neighbourhood of certain *subsets* common to the eventual limiting sets of the subsequences; this intersection of the subsequential limits is now *defined to be the limit of the original sequence.* A similar situation obtains, for example, in the solution of simultaneous equations: The solution of the equation $a_{11}x_{1}+a_{12}x_{2}=b_{1}$ for one of the variables $x_{2}$ say with $a_{12}\neq0$, is the set represented by the straight line $x_{2}=m_{1}x_{1}+c_{1}$ for all $x_{1}$ in its domain, while for a different set of constants $a_{21}$, $a_{22}$ and $b_{2}$ the solution is the entirely different set $x_{2}=m_{2}x_{1}+c_{2}$, under the assumption that $m_{1}\neq m_{2}$ and $c_{1}\neq c_{2}$. Thus even though the individual equations (subsequences) of the simultaneous set of equations (sequence) may have distinct solutions (limits), the solution of the equations is their common point of intersection.

Considered as sets in $X\times Y$, the discussion of convergence of a sequence of graphs $f_{n}\!:X\rightarrow Y$ would be incomplete without a mention of the convergence of a sequence of sets under the Hausdorff metric that is so basic in the study of fractals. In this case, one talks about the convergence of a sequence of compact subsets of the metric space $\mathbb{R}^{n}$ so that the sequences, as also the limit points that are the fractals, are compact subsets of $\mathbb{R}^{n}$. 