Errors, Failures, and Faults in the Context of Elementary Arithmetic

It is argued that setting one over zero to the upthorn symbol, elsewhere used to denote bottom, as is done in common meadows, is conceptually meaningful for elementary mathematics. We consider the arguments in its favour, for the restricted context of use in elementary arithmetic, to be stronger than arguments supporting one over zero equals zero, as in Suppes-Ono division and variants of it sometimes used in the model theory of fields as a branch of mathematical logic, or one over zero as an unsigned infinity, as proposed by Riemann and used in the design of wheel arithmetic, or one over zero as positive infinity, as in transrational arithmetic.