Sentence examples for rigorous foundation for from inspiring English sources

Like the axioms for geometry devised by Greek mathematician Euclid (c. 300 bce), the Peano axioms were meant to provide a rigorous foundation for the natural numbers (0, 1, 2, 3,…) used in arithmetic, number theory, and set theory.

This, together with the bold discoveries of the German mathematician Georg Cantor in set theory, made it clear that, to avoid further confusion and satisfactorily answer paradoxical results, a new and more rigorous foundation for mathematics was necessary.

For myself this feeling of dissatisfaction was so overpowering that I made a fixed resolve to keep meditating on the question till I should find a purely arithmetic and perfectly rigorous foundation for the principles of infinitesimal analysis.…I succeeded on November 24 , 1858

Mathematicians worked very hard to provide a rigorous foundation for Dirac's formal framework.

These TSIs offer a 0 100 scale providing continuous numerical classes of lake trophic states and a rigorous foundation for quantitative studies of the underlying causes of eutrophication.

Following the publication of Russell's paradox, Hilbert presented an address to the Third International Congress of Mathematicians in 1904, where, for the first time, he sketched his plan to provide a rigorous foundation for mathematics via syntactic consistency proofs.

While laying rigorous foundations for mathematics, 19th-century mathematicians discovered that the language of mathematics could be reduced to that of set theory (developed by Cantor), dealing with membership and equality, together with some rudimentary arithmetic, containing at least symbols for zero (0) and successor (S).

Indeed, the MWI has rigorous foundations for (i), the "physics part" of the theory; only part (ii), the correspondence with our experience, is approximate (just fine FAPP).

A rigorous foundation was eventually provided for infinitesimals by Robinson during the second half of the 20th Century, but infinitesimals are rarely used in contemporary physics.

Click here to order a copy for £7.99 It might seem logical that nonfiction, with its rigorous foundation in fact, would be a more persuasive instrument of social change than fiction; but I believe this is not the case.

That job was a rigorous foundation.