Sentence examples for as rational numbers from inspiring English sources

In other words, the fractions (known as rational numbers) are definitely countable.

Fractions of integers (with b nonzero) are known as rational numbers.

This is not as strange as it seems, as the rational numbers have exactly this property.

Using category theory and ideas from topology, he reformulated algebraic geometry so that it applies to commutative rings (such as the integers) and not merely fields (such as the rational numbers) as hitherto.

Using systematic generalizations, addition can also be defined on more abstract quantities, such as integers, rational numbers, real numbers and complex numbers and other abstract objects such as vectors and matrices.

The approach to the problem developed by Gauss, clarified and refined by Dirichlet, and pushed further by Kummer involves considering extensions of the (field of) rational numbers, as well as of the (ring of) "integers" contained in such extensions.

The geometric approach had led Eudoxus in the 4th century bce to define them as approximations by rational numbers (e.g., a series of nonrepeating decimals, as √2 = 1.414213... ).

Both took as given the set of rational numbers, and for the definition of R they relied on a certain totality of infinite sets of rational numbers (either sequences, or Dedekind cuts).

Being an irrational number, cannot be expressed exactly as a common fraction, although fractions such as 22/7 and other rational numbers are commonly used to approximate.

And in fact, in Dedekind's Nachlass explicit sketches of two now familiar constructions can be found: that of the positive and negative integers as (equivalence classes of) pairs of natural numbers; and that of the rational numbers as (equivalence classes of) pairs of integers (Sieg & Schlimm 2005, earlier Dugac 1976).

The theory Td, for example, of dense linear ordering (such as that of the rational numbers) is categorical in the countable cardinality.