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All transcendental real numbers (also known as real transcendental numbers or transcendental irrational numbers) are irrational numbers, ... (PDF). Rahmen der 79.
Transcendental number theory is a branch of number theory that investigates transcendental numbers (numbers that are not solutions of any polynomial equation with rational coefficients), in both qualitative and quantitative ways.
Download as PDF; Printable version; In other projects Wikidata item; ... Pages in category "Transcendental numbers" The following 16 pages are in this category, out ...
Download as PDF; Printable version; In other projects ... Help. This category is about the real numbers which are transcendental. All of those are irrational. ...
(A more elementary proof that e is transcendental is outlined in the article on transcendental numbers.) Alternatively, by the second formulation of the theorem, if α is a non-zero algebraic number, then {0, α} is a set of distinct algebraic numbers, and so the set { e 0 , e α } = {1, e α } is linearly independent over the algebraic numbers ...
This may be expressed as saying that if log α, log γ are linearly independent over the rationals, then they are linearly independent over the algebraic numbers. The generalisation of this statement to more general linear forms in logarithms of several algebraic numbers is in the domain of transcendental number theory.
The proof by contradiction used to prove the existence of transcendental numbers from the countability of the real algebraic numbers and the uncountability of real numbers. Cantor's December 2nd letter mentions this existence proof but does not contain it. Here is a proof: Assume that there are no transcendental numbers in [a, b].
The strong three exponentials conjecture meanwhile states that if x 1, x 2, and y are non-zero complex numbers with x 1 y, x 2 y, and x 1 /x 2 all transcendental, then at least one of the three numbers x 1 y, x 2 y, x 1 /x 2 is not in L ∗.