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Such a number is algebraic and can be expressed as the sum of a rational number and the square root of a rational number. Constructible number: A number representing a length that can be constructed using a compass and straightedge. Constructible numbers form a subfield of the field of algebraic numbers, and include the quadratic surds.
In mathematics, "rational" is often used as a noun abbreviating "rational number". The adjective rational sometimes means that the coefficients are rational numbers. For example, a rational point is a point with rational coordinates (i.e., a point whose coordinates are rational numbers); a rational matrix is a matrix of rational numbers; a rational polynomial may be a polynomial with rational ...
In simple terms, the Continuum Hypothesis (CH) states that the set of real numbers has minimal possible cardinality which is greater than the cardinality of the set of integers. That is, every set S ⊆ R {\displaystyle S\subseteq \mathbb {R} } of real numbers can either be mapped one-to-one into the integers or the real numbers can be mapped ...
The decimal fraction notation is a special way of representing rational numbers whose denominator is a power of 10. For instance, the rational numbers , , and are written as 0.1, 3.71, and 0.0044 in the decimal fraction notation. [100]
A rational algebraic expression (or rational expression) is an algebraic expression that can be written as a quotient of polynomials, such as x 2 + 4x + 4. An irrational algebraic expression is one that is not rational, such as √ x + 4.
A simple fraction (also known as a common fraction or vulgar fraction) [n 1] is a rational number written as a/b or , where a and b are both integers. [9] As with other fractions, the denominator (b) cannot be zero. Examples include 1 / 2 , − 8 / 5 , −8 / 5 , and 8 / −5 .
The fundamental question in algebraic number theory is on the extent to which the ring of (generalized) integers in a number field, where an "ideal" admits prime factorization, fails to be a PID. Among theorems concerning a PID, the most important one is the structure theorem for finitely generated modules over a principal ideal domain .
This category represents all rational numbers, that is, those real numbers which can be represented in the form: ...where and are integers and is ...