The effect of applying the equations to the term algebra is a
partitioning or quotienting
of the terms into equivalence classes; the equations enable us to say
that certain terms which are syntactically distinct do, nevertheless,
have the same meaning. (In the usual algebra of natural numbers, 2+2,
3+1,4,4*1 are all members of the equivalence class of 4).
Applying the equations E above to the term algebra 
, we find, for
example, that the following are all members of the equivalence class
of zero:
We can regard this class as a single entity (since every member has the same semantics) and refer to it as zero. Any other term would do to represent the class; zero is simply the shortest (and most intuitively clear). Again, some members of the equivalence class of T are
We can refer to this class as T, the representative form for the class.