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Number theory is the study of properties of the integers. Because of the fundamental nature of the integers in mathematics, and the fundamental nature of mathematics in science, the famous mathematician and physicist Gauss wrote: "Mathematics is the queen of the sciences, and number theory is the queen of mathematics." There are an abundance of simply formulated questions about the ...
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Hace 4 días · More specifically, while the Gelfond-Schneider theorem showed that \(a^b\) is transcendental for any algebraic \(a,b\) (other than the trivial cases \(a=0,1\) and \(b\) is rational), this is still a countable set of numbers.
Hace 3 días · In number theory, a Liouville number is a real number with the property that, for every positive integer , there exists a pair of integers with such that. Liouville numbers are "almost rational ", and can thus be approximated "quite closely" by sequences of rational numbers.
Hace 3 días · In mathematics, a transcendental number is a real or complex number that is not algebraic – that is, not the root of a non-zero polynomial of finite degree with rational coefficients. The best-known transcendental numbers are π and e. [1] [2] The quality of a number being transcendental is called transcendence .
Hace 3 días · Elliptic curves are curves defined by a certain type of cubic equation in two variables. The set of rational solutions to this equation has an extremely interesting structure, including a group law. The theory of elliptic curves was essential in Andrew Wiles' proof of Fermat's last theorem.
Hace 3 días · identify rational numbers (including fractions, decimals, and integers), find the position of a rational number on a number line, recognize the set of rational numbers ( ℚ), find a rational number at a specified point between two rational numbers.
