Information om | Engelska ordet NON-CONSTRUCTIVE

Exempel på hur man kan använda NON-CONSTRUCTIVE i en mening

• His proof of the well-ordering theorem, based on the powerset axiom and the axiom of choice, was not accepted by all mathematicians, mostly because the axiom of choice was a paradigm of non-constructive mathematics.
• However, it is also possible to give a Brouwerian counterexample to show that the statement is non-constructive.
• In contrast, a non-constructive proof of an impossibility claim would proceed by showing it is logically contradictory for all possible counterexamples to be invalid: at least one of the items on a list of possible counterexamples must actually be a valid counterexample to the impossibility conjecture.
• It might appear that this is the non-constructive equivalent of the constructive definition using iterated exponentiation; but the two definitions are equally non-constructive at steps indexed by limit ordinals, which represent transfinite recursion of a higher order than taking the supremum of an exponential series.
• Unreasonable, because the mathematical assumptions are economically unwarranted; ineffective because the mathematical formalisations imply non-constructive and uncomputable structures.

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