Please edit post #2, this is probably a typo Cos(A-B) - Cos(A-B) = 2SinASinB

Error spotted by Thuhina.

]]>"13. Introduction of the product. If M is a set different from 0 and a is anyone of its elements, then according to No.5 it is definite whether M = {a} or not. It is therefore always definite whether a given set consists of a single element or not.

Now let T be a set whose elements, M, N, R, . . ., are various (mutually disjoint) sets, and let S1 be any subset of its union ST. Then it is definite for every element M of T whether the intersection [M, 8 1 ] consists of a single element or not. Thus all those elements of T that have exactly one element in common with 8 1 are the elements of a certain subset T 1 of T, and it is again definite whether T 1 = T or not. All subsets S1 of ST that have exactly one element in common with each element of T then are, according to Axiom III, the elements of a set P = T, which, according to

Axioms III and IV, is a subset of union T and will be called the connection set [Verbindungsmenge] associated with T or the product of the sets M, N, R, . . .. If T = {M, N}, or T = {M, N, R}, we write T = MN, or T = MNR, respectively, for

short. "

I just do not understand why it is called "product" and how {M,N} can become MN here. Not in general therefore, but in this text. Thank you.]]>

for every natural number *n*. We call this function the *Dirichlet convolution* of *f* and *g*.

You are not required to memorize it. You can always look it up if necessary. Also, there are other methods to get roots that are more amenable to computation, these should be used when possible.

]]>Yes, I should have clarified. After you use the specified formula, you get the Rational # in between by: x+d, x+2d, x+3d...x+nd. To give an example, lets say we have to find 3 rational numbers between 2 and 3. Therefore: x=2 y=3 n=3. Thus, d= (3-2)/(3+1)=1/4. So the n numbers are: 2 1/4, 2 2/4 and 2 3/4. This is fairly obvious, I just wanted to give the generalized formula.

Yes I agree with you I also use this formula of rational number and I got the actual answer.

]]>Thank for sharing. Now i can also calculate only in 3 minutes.]]>