nction cannot be its own argument, whereas an operation can
take one of its own results as its base.

5.252 It is only in this way that the step from one term of a series
of forms to another is possible (from one type to another in the
hierarchies of Russell and Whitehead). (Russell and Whitehead did not
admit the possibility of such steps, but repeatedly availed themselves
of it.)

5.2521 If an operation is applied repeatedly to its own results, I speak
of successive applications of it. ('O'O'O'a' is the result of three
successive applications of the operation 'O'E' to 'a'.) In a similar
sense I speak of successive applications of more than one operation to a
number of propositions.

5.2522 Accordingly I use the sign '[a, x, O'x]' for the general term of
the series of forms a, O'a, O'O'a,.... This bracketed expression is a
variable: the first term of the bracketed expression is the beginning
of the series of forms, the second is the form of a term x arbitrarily
selected from the series, and the third is the form of the term that
immediately follows x in the series.

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 p