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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 ...
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.
Indian mathematicians made early contributions to the study of the concept of zero as a number, [5] negative numbers, [6] arithmetic, and algebra. [7] In addition, trigonometry [ 8 ] was further advanced in India, and, in particular, the modern definitions of sine and cosine were developed there. [ 9 ]
Entrance to NCERT campus on Aurobindo Marg, New Delhi. The National Curriculum Framework 2005 (NCF 2005) is the fourth National Curriculum Framework published in 2005 by the National Council of Educational Research and Training (NCERT) in India. Its predecessors were published in 1975, 1988, 2000.
This category represents all rational numbers, that is, those real numbers which can be represented in the form: ...where and are integers and is ...
An algebraic number is a number that is a root of a non-zero polynomial in one variable with integer (or, equivalently, rational) coefficients. For example, the golden ratio , ( 1 + 5 ) / 2 {\displaystyle (1+{\sqrt {5}})/2} , is an algebraic number, because it is a root of the polynomial x 2 − x − 1 .
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The set of rational numbers is not complete. For example, the sequence (1; 1.4; 1.41; 1.414; 1.4142; 1.41421; ...), where each term adds a digit of the decimal expansion of the positive square root of 2, is Cauchy but it does not converge to a rational number (in the real numbers, in contrast, it converges to the positive square root of 2).