constructive proofの例文

• This shows that non-constructive proofs can have constructive outcomes.
• Constructivism is a mathematical philosophy that rejects all but constructive proofs in mathematics.
• Meng also gave a less intricate constructive proof.
• Later, constructive proofs were found, which also supplied algorithms for finding the complementary edge.
• Because no such proof is known, the quoted statement must also not have a known constructive proof.
• I particularly like the fact that it's a constructive proof, not just an existence proof.
• Polynomials in Bernstein form were first used by Bernstein in a constructive proof for the Stone Weierstrass approximation theorem.
• Asserting that Cantor gave a non-constructive proof can lead to erroneous statements about the history of mathematics.
• The letters of December 2 and 7 lead to a non-constructive proof of the existence of transcendental numbers.
• Since these books view Cantor's proof as non-constructive, they do not mention his constructive proof.
• Also, it is not a constructive proof : it does not exhibit a concrete position that needs this many moves.
• The method of the proof suggested by Mergelyan is constructive, and remains the only known constructive proof of the result.
• Usually, decidability is proved by showing an algorithm that solves the problem ( i . e . a constructive proof ).
• :For a constructive proof, recall that an arithmetic progression looks like a + bn for some choice of a and b.
• A constructive proof of the existence part of the theorem is provided by any algorithm computing the Smith normal form of a matrix of integers.
• Some non-constructive proofs show that if a certain proposition is false, a contradiction ensues; consequently the proposition must be true ( proof by contradiction ).
• Certain constructive proofs exist, but they tend to require highly complicated ( i . e . fractal ) functions, and thus are not suitable for modeling approaches.
• Kellogg, Li, and Yorke turned Hirsch's proof into a constructive proof by observing that the retract is in fact defined everywhere except at the fixed points.
• It was Weierstrass who raised for the first time, in the middle of the 19th century, the problem of finding a constructive proof of the fundamental theorem of algebra.
• The Bernstein form was used in a constructive proof of the Weierstrass approximation theorem by Bernstein and has nowadays gained great importance in computer graphics in the form of B閦ier curves.