5.2523 The concept of successive applications of an operation is equivalent
to the concept 'and so on'.


5.253 One operation can counteract the effect of another. Operations can
cancel one another.


5.254 An operation can vanish (e.g. negation in 'PPp' : PPp = p).


5.3 All propositions are results of truth-operations on elementary
propositions. A truth-operation is the way in which a truth-function is
produced out of elementary propositions. It is of the essence of truth-
operations that, just as elementary propositions yield a truth-function of
themselves, so too in the same way truth-functions yield a further truth-
function. When a truth-operation is applied to truth-functions of
elementary propositions, it always generates another truth-function of
elementary propositions, another proposition. When a truth-operation is
applied to the results of truth-operations on elementary propositions,
there is always a single operation on elementary propositions that has the
same result. Every proposition is the result of truth-operations on
elementary propositions.


5.31 The schemata in 4.31 have a meaning even when 'p', 'q', 'r', etc. are
not elementary propositions. And it is easy to see that the propositional
sign in 4.442 expresses a single truth-function of elementary propositions
even when 'p' and 'q' are truth-functions of elementary propositions.