A form of the reductio ad absurdum argument, known as indirect proof or reductio ad impossibile, is one that proves a proposition by showing that its denial conjoined with other propositions previously proved or accepted leads to a contradiction.
Dr. Ngo, the first Vietnamese mathematician to receive a Fields, proved a proposition, or fundamental lemma, that underlies a three-decade effort by mathematicians to link geometry and number theory.
But first we prove a proposition giving some insight into the structure of this type of mappings.
We had proved a proposition in [6] by using a function and we get a right-hand side inequality, similar to (2.7).
We prove a proposition asserting conditions under which the robustness curves for two different designs will cross one another, entailing the potential for reversal of preference between the two designs.
A proof-theoretic reduction of a theory T to a theory S shows that, as far as a certain class of propositions is concerned, if T proves a proposition, then S proves it too, and the proof of this fact is itself finitary.
Grounded research combines two data analysis processes; all data are coded and systematically analyzed to verify or prove a proposition [ 25].
It remains unlikely to be disproved completely in the near future, in part because proving a negative proposition is difficult to do and also because negative data can be seen as unwelcome news.
