## Definition Edit

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

Failed to parse (lexing error): 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 Edit

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