Sentence examples for classical proof from inspiring English sources

Given what are classically two variants of a single set-theoretic principle, their classical proof of equivalence requires at some point an instance of the excluded middle.

The proof follows the classical proof of De Finetti's theorem, the main technical tool being a noncommutative Lp-inequality for i.i.d.i.d

A classical proof mass actuator is formed by a coil magnet linear motor, with either the magnet or the armature-coil proof mass suspended on soft springs.

For a given spectrum and set of lengths, the existence of such frames is characterized by the Schur Horn Theorem they exist if and only if the spectrum majorizes the squared lengths the classical proof of which is nonconstructive.

A slick classical proof goes as follows.

For a classical proof using different arguments, see, e.g., [3].

The resulting picture is one where all these things have internal structure, their algebraic properties are axiomatized, and one can therefore reason about them in a classical proof-theoretical way.

Proof terms in \(\mathsf{LP}\) are nothing but BHK terms understood as classical proofs.

In fact, the intuitionistic proofs of both statements are complex and deviate from the classical proofs (Coquand 1995, Veldman 2004).

The classical proofs are intuitionistically not acceptable because of the way they depend on PEM; the intuitionistic proofs are classically not acceptable because they depend on reflection on the structure of mental proofs.

In this work, we introduce a metric type structure in cone metric spaces and show that classical proofs do carry almost identically in these metric spaces.