And what if the only reality in existence was virtual reality? The individual identity in virtual reality has always been studied with regards to individual identity in reality. Indeed, the individual in virtual reality is considered as a real individual to whom we removed fundamental features: spatial unity (Leibniz) and temporal identity or sameness (Ricoeur, 1990). In other words, a virtual ...

We say an algebraic object or property over a field k is arithmetic if it becomes trivial or vanishes after finite separable base extension. Since such objects or properties owe their existence to the presence of “arithmetic gaps” in k, i.e., the failure of k to be algebraically closed, we view them as responses to specific arithmetic properties of k, and we study them in order to gain insight ...

1. A function is arithmetic if it is defined on the positive integers. Those arithmetic functions which assume real values and satisfy f(ab)-f(a)+f(b) for mutually prime integers a, b are classically called additive. The following examples illustrate the interest of these functions, both for themselves and for their applications. An additive function is defined by its values on the prime powers...