Since mathematical analysis is essentially the science of the
continuum, it would seem that every course in analysis should
begin, logically, with the study of irrational numbers. I have
supposed, however, that the student is already familiar with that
subject. The theory of incommensurable numbers is treated in so
many excellent well-known works f that I have thought it useless to
enter upon such a discussion. As for the other fundamental notions
which lie at the basis of analysis, such as the upper limit, the
definite integral, the double integral, etc., I have endeavored to
treat them with all desirable rigor, seeking to retain the
elementary character of the work, and to avoid generalizations
which would be superfluous in a book intended for purposes of
instruction.
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