Changes

</ol>

</ol>

As a result of marking the distinction between empty and significant sentences, that is, by categorizing each of these three classes of strings as an entity unto itself and by conceptualizing the whole of its membership as falling under a distinctive symbol, one obtains an equation of sets that connects the three languages being marked:

As a result of marking the distinction between empty and significant sentences,

that is, by categorizing each of these three classes of strings as an entity

unto itself and by conceptualizing the whole of its membership as falling

under a distinctive symbol, one obtains an equation of sets that connects

the three languages being marked:

SPARCE = PARCE - EPARCE.

| <math>\operatorname{SPARCE} \ = \ \operatorname{PARCE} \ - \ \operatorname{EPARCE}</math>

In sum, one has the disjoint union:

In sum, one has the disjoint union:

PARCE   = EPARCE |_| SPARCE.

| <math>\operatorname{PARCE} \ = \ \operatorname{EPARCE} \ \cup \ \operatorname{SPARCE}</math>

|}

For brevity in the present case, and to serve as a generic device

For brevity in the present case, and to serve as a generic device

in any similar array of situations, let the symbol "S" be used to

in any similar array of situations, let the symbol "S" be used to