Understanding Transcendal Numbers: Importance and Examples

[ziad1985]

Can someone please explain what are Transcendal Numbers are?
and why they are so important?

 

[TD]

A transcendental number is a number which isn't a root of any polynomial with integer coefficients. It's therefore not an algebraic number (of any degree).

All transcendental numbers are irrational but the converse is not true. For example, $\sqrt 2$ is irrational but is a solution of $x^2 = 2$.

 

[arildno]

They are important in that almost all real numbers are transcendental.

 

[ziad1985]

That means it should include e and Pi ?
I read one time that e and pi are belived to be a root of some kind of an equation.

 

[TD]

That means it should include e and Pi ?
I read one time that e and pi are belived to be a root of some kind of an equation.

e and pi are both transcendental.

 

[matt grime]

e and pi certainly are the roots of 'some kinds of equation', just not any polynomial over Q. They are roots if $x^2-(e+\pi)x+e\pi$, for instance.