I was thinking about math as usual, so I decided to try to write about it to see if it promotes my understanding any, so bear with me. Group theory proves the behaviour of equations by examining the symmetries of their solutions. For instance an equilatoral triangle has 6 different symmetries: F, R, I, R^2, FR and FR^2. Because it has 3 points and 3! = 6. Any other compostitions of elements, F, R, or I reduce to fall under these 6, because of the following: R^3 = I, F^2 = I and RF = FR^2.

On a different topic: Epsilon - Delta defintition of Limits
The limit as x goes to 2 of x^2 =4. Let E>0 be given(fixed but arbitary) Note that you can always make delta smaller than nessesary by taking the minimum. Hence x1^2 = 4-E, therefore x1=sqrt(4-E), suppose E<4. and x2^2 = 4+E, thereforex2=sqrt(4+E). Let delta be the minimum of {2-x1, x2-2}. Note that delta is always greater than 0. Suppose that abs(x-2) < delta. Now follow through two cases, to find abs(x^2-4)< E.