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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 ...
In mathematics, a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials. The coefficients of the polynomials need not be rational numbers ; they may be taken in any field K .
In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on rational and real numbers. A field is thus a fundamental algebraic structure which is widely used in algebra, number theory, and many other areas of mathematics.
The meaning of the terms "rational" and "irrational" in academic discourse often differs from how they are used in everyday language. Examples of behaviors considered irrational in ordinary discourse are giving into temptations , going out late even though one has to get up early in the morning, smoking despite being aware of the health risks ...
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.
Q – rational numbers. QED – "Quod erat demonstrandum", a Latin phrase used at the end of a definitive proof. QEF – "Quod erat faciendum", a Latin phrase sometimes used at the end of a geometrical construction.
A rational number is a number that can be expressed as a fraction with an integer numerator and a positive integer denominator. Negative denominators are allowed, but are commonly avoided, as every rational number is equal to a fraction with positive denominator.
In mathematics, exponentiation is an operation involving two numbers: the base and the exponent or power. ... If r is a positive rational number, 0 r = 0, by definition.