Tags » Algebraic

Diophantine Approximation: Liouville’s Theorem

Diophantine approximation deals with the approximation of real numbers by rational numbers.

Liouville’s Theorem

In the 1840’s Liouville obtained the first lower bound for the approximation of algebraic numbers: 169 more words


Transcendental Numbers

A transcendental number is a number that is real or complex, but it not algebraic, meaning that it is not the root of a polynomial with non-zero integer coefficients. 223 more words


Transitivity of Algebraic Extensions

Let be a tower of fields. If and are algebraic, then is algebraic.


(Hungerford pg 237, reworded)

Let . Since is algebraic over , there exists some () such that… 41 more words


Arithmetic Operations

There are only 4 binary operations which we call “arithmetic operations”. These are:

  • Addition (+)
  • Subtractions (-)
  • Multiplication (×)
  • Division (÷)

Reading this fact, an obvious question is: 398 more words

Problem Solving