# Elementary Functions as a Solvable Group

• Oct 31st 2006, 01:08 PM
ThePerfectHacker
Elementary Functions as a Solvable Group
I am not so happy with the defintion for a elementary function viewed as a finite number of combinations of addition, subtraction, multiplication, division and roots.

It sounds familar to the meaning of a "solutions by radicals" of a polynomial. Though it does has an alternate defintion, it is defined as a solvable group. Is there a way to define these functions also as some solvable group? The only thing I can think of is that the number of solutions to a polynomial is finite. Where the number of elementary functions is not. Thus, the compositions series does not exist. But if you can find one will it not make the proves based on showing there is no such elementary function simpler?

This is my 31:):)th Post!!!
• Oct 31st 2006, 01:33 PM
topsquark
Quote:

Originally Posted by ThePerfectHacker
I am not so happy with the defintion for a elementary function viewed as a finite number of combinations of addition, subtraction, multiplication, division and roots.

It sounds familar to the meaning of a "solutions by radicals" of a polynomial. Though it does has an alternate defintion, it is defined as a solvable group. Is there a way to define these functions also as some solvable group? The only thing I can think of is that the number of solutions to a polynomial is finite. Where the number of elementary functions is not. Thus, the compositions series does not exist. But if you can find one will it not make the proves based on showing there is no such elementary function simpler?

This is my 31:):)th Post!!!

Just to get this straight, are you suggesting that we no longer consider the sine function elementary?

-Dan
• Oct 31st 2006, 06:07 PM
ThePerfectHacker
Quote:

Originally Posted by topsquark
Just to get this straight, are you suggesting that we no longer consider the sine function elementary?

-Dan

No, it is.

To be elementary we define a function as a finite sum difference multiplication division and composition of:
polynomials,trigonometric,inverse trigonometric, exponential, logarithmic.
• Jul 13th 2007, 12:19 PM
ThePerfectHacker
I guess I was right :) there is such an area in mathematics.
Look Here.