On Transcendental Numbers

نویسنده

  • Florin F. Nichita
چکیده

Transcendental numbers play an important role in many areas of science. This paper contains a short survey on transcendental numbers and some relations among them. New inequalities for transcendental numbers are stated in Section 2 and proved in Section 4. Also, in relationship with these topics, we study the exponential function axioms related to the Yang-Baxter equation.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Math 249 A Fall 2010 : Transcendental Number Theory

α is algebraic if there exists p ∈ Z[x], p 6= 0 with p(α) = 0, otherwise α is called transcendental . Cantor: Algebraic numbers are countable, so transcendental numbers exist, and are a measure 1 set in [0, 1], but it is hard to prove transcendence for any particular number. Examples of (proported) transcendental numbers: e, π, γ, e, √ 2 √ 2 , ζ(3), ζ(5) . . . Know: e, π, e, √ 2 √ 2 are transce...

متن کامل

Transcendental Numbers and Zeta Functions

The concept of “number” has formed the basis of civilzation since time immemorial. Looking back from our vantage point of the digital age, we can agree with Pythagoras that “all is number”. The study of numbers and their properties is the mathematical equivalent of the study of atoms and their structure. It is in fact more than that. The famous physicist and Nobel Laureate Eugene Wigner spoke o...

متن کامل

Formalizing a Proof that e is Transcendental

A transcendental number is one that is not the root of any non-zero polynomial having integer coefficients. It immediately follows that no rational number q is transcendental, since q can be written as a/b where a and b are integers, and thus q is a root of bx − a. Furthermore, the transcendentals are a proper subset of the irrationals, since for example the irrational √ 2 is a root of x − 2. T...

متن کامل

Transcendence of e and π

When proving it is impossible to ‘square’ the circle by a ruler–and–compass construction we have to appeal to the theorem that π is transcendental. It is our goal to prove this theorem. Since the algebraic numbers are the roots of integer polynomials, they are countably many. Cantor’s proof in 1874 of the uncountability of the real numbers guaranteed the existence of (uncountably many) transcen...

متن کامل

Yet Another Direct Proof of the Uncountability of the Transcendental Numbers

The most known proof of uncountability of the transcendental numbers is based on proving that A is countable and concluding that R\A is uncountable since R is. Very recently, J. Gaspar [1] gave a nice “direct” proof that the set of transcendental numbers is uncountable. In this context, the word direct means a proof which does not follow the previous steps. However, we point out that his proof ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Axioms

دوره 3  شماره 

صفحات  -

تاریخ انتشار 2014