In mathematical logic, Peano–Russell notation was Bertrand Russell's application of Giuseppe Peano's logical notation to the logical notions of Frege and was used in the writing of Principia Mathematica in collaboration with Alfred North Whitehead:[1] "The notation adopted in the present work is based upon that of Peano, and the following explanations are to some extent modelled on those which he prefixes to his Formulario Mathematico."
(Chapter I: Preliminary Explanations of Ideas and Notations, page 4)In the notation, variables are ambiguous in denotation, preserve a recognizable identity appearing in various places in logical statements within a given context, and have a range of possible determination between any two variables which is the same or different.
An asserted proposition is either true or an error on the part of the writer.
[5] In addition to the logical product, dots are also used to show groupings of functions of propositions.
The notation includes definitions as complex functions of propositions, using the equals sign "=" to separate the defined term from its symbolic definition, ending with the letters "Df".