Equinumerosity

Before moving ahead to the discussion of this principle, the reader should convince him - or herself of the following four facts: (1) that the material equivalence of two concepts implies their equinumerosity, (2) that equinumerosity is reflexive, (3) that equinumerosity is symmetric, and (4) that equinumerosity is transitive. ❋ Zalta, Edward N. (2009)

In this example, no relation R can satisfy the definition of equinumerosity. ❋ Zalta, Edward N. (2009)

The proofs of these facts, in each case, require the identification of a relation that is a witness to the relevant equinumerosity claim. ❋ Zalta, Edward N. (2009)

In order to state the definition of equinumerosity, we shall employ the well-known logical notion ˜there exists a unique x such that φ (x)™. ❋ Zalta, Edward N. (2009)

The definition of equinumerosity, or of the existence of a one to one mapping between two classes, also called ❋ Linsky, Bernard (2009)

From here the step is not far to Dedekind's view that equipollence is a sufficient condition for equinumerosity. ❋ Gerard Varni (2009)