For example, in the following sequence of row operations ( where multiple elementary operations might be done at each step ), the third and fourth matrices are the ones in row echelon form, and the final matrix is the unique reduced row echelon form.
32.
Goodman, Richard Milton Martin, and Willard Quine all advocated reasoning about collectivities by means of a theory of " virtual sets " ( see especially Quine 1969 ), one making possible all elementary operations on sets except that the universe of a quantified variable cannot contain any virtual sets.
