The proof resolves a nearly 80-year-old problem known as the Duffin-Schaeffer conjecture. In doing so, it provides a final answer to a question that has preoccupied mathematicians since ancient times: ...

Mathematics students face challenges with rational and irrational numbers. Understanding the principles and patterns simplifies this concept. Rational numbers can be fractions of integers. Irrational ...

The ancient scholar Hippasus of Metapontum was punished with death for his discovery of irrational numbers—or at least that’s the legend. What actually happened in the fifth century B.C.E. is far from ...

IN the first of these tracts Prof. Dedekind gives a theory of irrational numbers and of the arithmetical continuum which is logically perfect, and in form, perhaps, more simple and direct than any ...