"The way in which the irrational numbers are usually introduced is based directly upon the conception of extensive mag…"

"That such comparisons with non-arithmetic notions have furnished the immediate occasion for the extension of the numb…"

"I regard the whole of arithmetic as a necessary, or at least natural, consequence of the simplest arithmetic act, tha…"

"As professor in the Polytechnic School [autumn of 1858] in Zurich I found myself for the first time obliged to lectur…"

"The statement is so frequently made that the differential calculus deals with continuous magnitude, and yet an explan…"

"What advantage will be gained by even a purely abstract definition of real numbers of a higher type, I am as yet unab…"

"Addition is the combination of any arbitrary repetitions of the above-mentioned simplest act into a single act; from …"

"If a, c are two different numbers, there are infinitely many different numbers lying between a, c."

"If a is any definite number, then all numbers of the system R fall into two classes, A1 and A2, each of which contain…"

"Just as negative and fractional rational numbers are formed by a new creation, and as the laws of operating with thes…"