Identity similarity

Definition
Given a universe set $$E$$, the identity similarity function is a function $$IdSim:E\times E \longrightarrow \{0,1\}$$ defined as

$$ IdSim(x,y)= \left\{% \begin{array}{ll} 1, & \hbox{if $x=y$;} \\ 0, & \hbox{if $x\neq y$.} \\ \end{array}% \right. $$

This similarity could be applied to every set $$E$$ but give no information about the grade of resemblance between $$x$$ and $$y$$ when they are different.

Examples

 * $$IdSim(0,0) = 1$$.
 * $$IdSim(0,1) = 0.$$.
 * $$IdSim(\mbox{'car'},\mbox{'cars'}) = 0$$.
 * $$IdSim(\mbox{'car'},\mbox{'auto'}) = 0$$.