Sentence examples for proofs proofs from inspiring English sources

He was the first to doubt the significance of nonconstructive existence proofs (proofs that show something must exist, often by using a proof through contradiction, but that give no method of producing them), and for many years he carried on a polemic against the analytic school of the German mathematician Karl Weierstrass concerning these proofs and other points of classical analysis.

"Do you have any proof?" "Proof?" "Proof".

Where is the proof?" "Proof?" I said, incredulous.

Topics include direct proof, proof by contrapositive, proof by contradiction, many applications of mathematical induction, constructing good definitions, and useful writing habits.

MacKenzie argues that our culture now contains two ideals of proof: proof as traditionally conducted by human mathematicians, and formal, mechanized proof.

Here was proof — proof that as a component of "the media," the liberal blogosphere is as important to the Democratic Party as CNN or MSNBC.

Proof Proof is shifted to Section 4.

Proof Proof follows directly from Proposition 4.1.

Proof Proof follows from Definition 1.1.

Proof Proof is similar to the proof of Theorem 5.

Proof Proof of formula (10) follows now immediately from (7). □.