Question

in Philosophy 160 Deductive Logic II,

Prove in predicate logic with identity that there is at least one solution to Hilbert's set of simultaneous equations from the premise that there's exactly one solution to them. Do not combine two steps into one. Sx : x is a solution to Hilbert's set of simultaneous equations.

Answer 1

Hilbert's tenth problem is the tenth on the list of mathematical problems that the German mathematician David Hilbert posed in 1900. It is the test to give a general calculation which, for any given Diophantine condition (a polynomial condition with whole number coefficients and a limited number of questions), can choose whether the condition has an answer with all questions taking whole number qualities.

Hilbert's tenth issue has been explained, and it has a negative answer: such a general calculation does not exist. This is the aftereffect of joined work of Martin Davis, Yuri Matiyasevich, Hilary Putnam and Julia Robinson which traverses 21 years, with Yuri Matiyasevich finishing the hypothesis in 1970. The words "process" and "limited number of activities" have been interpreted as meaning that Hilbert was requesting a calculation. The expression "sane whole number" essentially alludes to the numbers, positive, negative or zero: 0, ±1, ±2, so Hilbert was requesting a general calculation to choose whether a given polynomial Diophantine condition with number coefficients has an answer in whole numbers. Hilbert's problem is not concerned with finding the solutions. It just asks whether, all in all, we can choose whether at least one arrangements exist. The response to this inquiry is negative, as in no "procedure can be conceived" for addressing that question. In present day terms, Hilbert's tenth issue is an undecidable issue. In spite of the fact that it is far-fetched that Hilbert had considered such a plausibility, before proceeding to list the issues, he did perceptively comment: It just asks whether, all in all, we can choose whether at least one arrangements exist. The response to this inquiry is negative, as in no "procedure can be conceived" for addressing that question. In present day terms, Hilbert's tenth issue is an undecidable issue. In spite of the fact that it is far-fetched that Hilbert had considered such a plausibility, before proceeding to list the issues, he did perceptively comment: Proving the 10th problem undecidable is then a valid answer even in Hilbert's terms, since it is a proof about "the impossibility of the solution.