Proof Mining - Mathematics, Algorithms and Proofs
Proof Mining - Mathematics, Algorithms and Proofs
Proof Mining - Mathematics, Algorithms and Proofs
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
<strong>Proof</strong> <strong>Mining</strong><br />
Necessity of total boundedness: Let B be the unit ball<br />
C[0, 1]. B is bounded <strong>and</strong> constructively representable.<br />
By Weierstraß’ theorem<br />
BA ⊢ ∀f ∈ B∃n ∈ IN(n code of p ∈ Q[X] s.t. p − f∞ < 1<br />
2 )<br />
but no uniform bound on ∃n : take fn := sin(nx).<br />
Ulrich Kohlenbach 17