 Meanwhile the German mathematician Karl Weierstrass (1815–97) was completing the banishment of spatiotemporal intuition, and the infinitesimal, from the foundations of analysis. To instill complete logical rigor Weierstrass proposed to establish mathematical analysis on the basis of number alone, to  “arithmetize”[28]  it—in effect, to replace the continuous by the discrete. “Arithmetization” may be seen as a form of mathematical atomism. In pursuit of this goal Weierstrass had first to formulate a rigorous “arithmetical” definition of real number. He did this by defining a (positive) real number to be a countable set of positive rational numbers for which the sum of any finite subset always remains below some preassigned bound, and then specifying the conditions under which two such “real numbers” are to be considered equal, or strictly less than one another.