Increasingly a number of mathematical proofs have relied on global optimization problems solved using branch-and-bound algorithms with interval computations; it is therefore extremely important to have a mathematically correct implementation of interval arithmetic.
In fact, before conjectural statement and mathematical proof, we have first checked the simple case c± = 0, for which ρ 12 ± = ± 1, and have verified numerically the formulas (4.5) in the general case.
Further, I might be a priori justified in believing the conclusion of some mathematical proof I have constructed, but that justification can be defeated by the testimony of excellent mathematicians who tell me that the proof is unsound.
Some mathematical proofs make our conclusions reliable.
Because of the formal success of his logical theory, Aristotle also considers most mathematical proofs as having the form of a universal affirmative syllogism, namely Barbara.
For now, Dr. Rabin's idea is simply a scheme backed up by a mathematical proof that he has been presenting to scientists at seminars.
Proponents of the mathematical conception of the standard of proof have stood their ground even while acknowledging that weight has a role to play in the Bayesian analysis of probative value and the sufficiency of evidence.
Firstly the mathematical relation between the interconnection matrix and the library pattern matrix, and the stability of the EAPNN with infinite precision data have been studied, strictly mathematical proofs for them have been given.
In Turing's presentation, intuition is in practice present in every part of a mathematician's thought, but when mathematical proof is formalised, intuition has an explicit manifestation in those steps where the mathematician sees the truth of a formally unprovable statement.
