Axioms Quote by Hans Reichenbach

The concept of congruence in Euclidean geometry is not exactly the same as that in non-Euclidean geometry. ..."Congruent" means in Euclidean geometry the same…

— Hans Reichenbach

“The axiom of equality states that x always equals x: it assumes that if you have a conceptual thing named x, that it must…

— Hanya Yanagihara

An axiomatic system establishes a reverberating relationship between what a mathematician assumes (the axioms) and what he or she can derive (the theorems). In…

— David Berlinski

Thus number may be said to rule the whole world of quantity, and the four rules of arithmetic may be regarded as the complete…

— James Clerk Maxwell

The word 'definition' has come to have a dangerously reassuring sound, owing no doubt to its frequent occurrence in logical and mathematical writings.

— Willard Van Orman Quine

“Even in the realm of pure mathematics, the mathematician may use any set of symbols he desires within any given region of space-time; he…

— Fulton J. Sheen

[Mathematics is] purely intellectual, a pure theory of forms, which has for its objects not the combination of quantities or their images, the numbers,…

— Hermann Hankel

The numbers may be said to rule the whole world of quantity, and the four rules of arithmetic may be regarded as the complete…

— Anonymous

An axiomatic system comprises axioms and theorems and requires a certain amount of hand-eye coordination before it works. A formal system comprises an explicit…

— David Berlinski

The only thing that might have annoyed some mathematicians was the presumption of assuming that maybe the axiom of choice could fail, and that…

— Alonzo Church

Mathematicians are like lovers. Grant a mathematician the least principle, and he will draw from it a consequence which you must also grant him,…

— Bernard le Bovier de Fontenelle

If you want to be an artist in the long run, it isn't necessarily a good axiom to repeat formulas over and over until…

— Lindsey Buckingham