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

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

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

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

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

**Proof:**

(Hungerford pg 237, reworded)

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

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