Transcendental number

Transcendental numbers | Articles containing proofs

In mathematics, a transcendental number is a 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. Though only a few classes of transcendental numbers are known—partly because it can be extremely difficult to show that a given number is transcendental—transcendental numbers are not rare. Indeed, almost all real and complex numbers are transcendental, since the algebraic numbers comprise a countable set, while the set of real numbers and the set of complex numbers are both uncountable sets, and therefore larger than any countable set. All transcendental real numbers (also known as real transcendental numbers or transcendental irrational numbers) are irrational numbers, since all rational numbers are algebraic. The converse is not true: not all irrational numbers are transcendental. Hence, the set of real numbers consists of non-overlapping rational, algebraic non-rational and transcendental real numbers. For example, the square root of 2 is an irrational number, but it is not a transcendental number as it is a root of the polynomial equation x2 − 2 = 0. The golden ratio (denoted or ) is another irrational number that is not transcendental, as it is a root of the polynomial equation x2 − x − 1 = 0. The quality of a number being transcendental is called transcendence. (Wikipedia).

Transcendental Functions 19 The Function exp e.mp4

Euler's number to the power x.

From playlist Transcendental Functions

Transcendental Numbers

Transcendental Numbers In this video, I define the concepts of algebraic and transcendental numbers, which have to do with roots of polynomials. In particular, I show that the number ((2^1/2 - 3)/5)^1/3, even though complicated-looking, is algebraic. Enjoy! Check out my Real Numbers Play

From playlist Real Numbers

Transcendental Functions 19 The Function a to the power x.mp4

The function a to the power x.

From playlist Transcendental Functions

Transcendental Functions 4 Two Main Logarithmic Bases.mov

Logarithms with base 10 and Euler's number or the natural logarithm.

From playlist Transcendental Functions

Transcendental Functions 14 Derivative of Natural Log of x Example 3.mov

More examples to work through.

From playlist Transcendental Functions

Are they irrational? Transcendental? | Epic Math Time

Showing that a number is transcendental can be difficult. While π and e have a deep connection involving exponentiation, other combinations of them, like π + e, are not as well understood. Follow me on Instagram for previews, behind-the-scenes, and more content!: http://instagram.com/epic

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Transcendental Functions 22 The integral of e to the power u.mp4

The integral of e to the power u.

From playlist Transcendental Functions

Transcendental Functions 18 More Examples 2.mov

More example problems.

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Transcendental Functions 21 The Derivative of e to the power x.mp4

The derivative of e to the power x.

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"Transcendental Number Theory: Recent Results and Open Problems" by Prof. Michel Waldschmidt

This lecture will be devoted to a survey of transcendental number theory, including some history, the state of the art and some of the main conjectures.

From playlist Number Theory Research Unit at CAMS - AUB

Transcendental numbers powered by Cantor's infinities

In today's video the Mathologer sets out to give an introduction to the notoriously hard topic of transcendental numbers that is both in depth and accessible to anybody with a bit of common sense. Find out how Georg Cantor's infinities can be used in a very simple and off the beaten track

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FIT2.3.2. Cardinality and Transcendentals

Field Theory: We show that the set of algebraic numbers is countable and that any extension of a countable field F by a transcendental is countable. We then give an overview of known results on transcendental numbers.

From playlist Abstract Algebra

Galois theory: Field extensions

This lecture is part of an online course on Galois theory. We review some basic results about field extensions and algebraic numbers. We define the degree of a field extension and show that a number is algebraic over a field if and only if it is contained in a finite extension. We use thi

From playlist Galois theory

Algebraic numbers are countable

Transcendental numbers are uncountable, algebraic numbers are countable. There are two kinds of real numbers: The algebraic numbers (like 1, 3/4, sqrt(2)) and the transcendental numbers (like pi or e). In this video, I show that the algebraic numbers are countable, which means that there

From playlist Real Numbers

Liouville's number, the easiest transcendental and its clones (corrected reupload)

This is a corrected re-upload of a video from a couple of weeks ago. The original version contained one too many shortcut that I really should not have taken. Although only two viewers stumbled across this mess-up it really bothered me, and so here is the corrected version of the video, ho

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Galois theory: Transcendental extensions

This lecture is part of an online graduate course on Galois theory. We describe transcendental extension of fields and transcendence bases. As applications we classify algebraically closed fields and show hw to define the dimension of an algebraic variety.

From playlist Galois theory

Transcendental Functions 18 More Examples 1.mov

Transcendental number

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