Grasping Infinity by Finite Sets

Abstract

We show that the existence of an infinite set can be reduced to the existence of finite sets "as big as we will", provided that a multivalued extension of the relation of equipotence is admitted. In accordance, we modelize the notion of infinite set by a fuzzy subset representing the class of (finite) wide sets.Mathematics Subject Classification: 03B52, 03372, 04A72.

Multivalued Logic to Transform Potential into Actual Objects

“…In accordance, we call wide set theory the proposed theory T . The following proposition was proved in [7]. Then, I(INF )(x) = cr(x)/(cr(x) + 1).…”

“…In some previous papers we explore this idea in the particular frameworks of pointless geometry (see [8], [9] and [11]) and set theory (see [7]). …”