5.25 The occurrence of an operation does not characterize the sense of a
proposition. Indeed, no statement is made by an operation, but only by its
result, and this depends on the bases of the operation. (Operations and
functions must not be confused with each other.)


5.251 A function 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.