Facts about e (1 Viewer)

[buchanan]

I made a file, "Facts About e" below.

Maybe your teacher has told you everything in it. And maybe not.

http://www.angelfire.com/planet/threeunit/factsaboute.pdf

(updated on Feb. 9, 2007)

 

[buchanan]

I updated it yesterday and added the last two identities.

There's also more detailed notes at

http://www.angelfire.com/planet/threeunit/e.pdf

 

[Mill]

Both documents are a useful read.

But the second pdf is in bad need of typing!

(I know you didn't create it).

 

[buchanan]

Actually, I did create it. I'm a messy handwriter so most of my stuff is typed. But there are a few exceptions and this is one of them. Maybe I'll type it up sometime.

 

[Mill]

I assumed because usually you type your documents (as you said).

Silly me!

 

[ssglain]

That was an interesting read. Thanks for sharing.

 

[bos1234]

what does transcendental mean?

 

[darkliight]

We all know what a polynomial is by now. Well, a number is algebraic if it is the solution to some (non-zero) polynomial equation with rational coefficients.

The classical example is sqrt(n), for any rational number n. The polynomial equation x^2 - n = 0 certainly has rational coefficients. Since sqrt(n) satisfies this equation, it is algebraic.

A number is transcendental if it is not algebraic. So saying that e is transcendental is saying that there is NO (non-zero) polynomial equation with rational coefficients that has e as its solution.