Infinitesimals serve as the 'glue' that causes points on a continuous line to lose their individual identity, which is essential to a proper conception of continuity

Peirce’s conception of the number continuum is also notable for the presence in it of an abundance of infinitesimals, Peirce championed the retention of the infinitesimal concept in the foundations of the calculus, both because of what he saw as the efficiency of infinitesimal methods, and because he regarded infinitesimals as constituting the “glue” causing points on a continuous line to lose their individual identity.