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.

Frege's Logic, Theorem, and Foundations for Arithmetic Zalta, Edward N. 2009

In this example, no relation R can satisfy the definition of equinumerosity.

Frege's Logic, Theorem, and Foundations for Arithmetic 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.

Frege's Logic, Theorem, and Foundations for Arithmetic 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)™.

Frege's Logic, Theorem, and Foundations for Arithmetic Zalta, Edward N. 2009

The definition of equinumerosity, or of the existence of a one to one mapping between two classes, also called

Logical Constructions Linsky, Bernard 2009

From here the step is not far to Dedekind's view that equipollence is a sufficient condition for equinumerosity.

Slices of Matisse gerard varni 2009