ABSTRACT
The word continuity has borne among philosophers, especially since the time of Hegel, a meaning totally unlike that given to it by Cantor. This chapter discusses the mathematical meaning. Of the arithmetical continuum, M. Poincare justly remarks: “The continuum thus conceived is nothing but a collection of individuals arranged in a certain order, infinite in number, it is true, but external to each other. This is not the ordinary conception, in which there is supposed to be, between the elements of the continuum, a sort of intimate bond which makes a whole of them, in which the point is not prior to the line, but the line to the point. Numbers are entities whose nature can be established beyond question; and among numbers, the various forms of continuity which occur cannot be denied without positive contradiction.
