I have noticed that there are some symbols that are used in Modern (abstract) Algebra, that aren't necessarily listed in the math reference. "oplus", indicating a direct product between 2 groups, is one such example. I would like to track down a few others.

My most pressing need, is the sign for "is isomorphic to". (a tilde above an equal sign) How do I make this?

Please help.

I didn't find the right solution from the Internet.

References:-

https://forum.openoffice.org/en/forum/viewtopic.php?f=12&t=93851

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Thanks!

]]>(Angles are given in degrees, 90 degrees, 180 degrees etc.)

I.

Sin(-θ)=-Sinθ

Cos(-θ) = Cosθ

tan(-θ) = -tanθ

cot(-θ) = -cotθ

sec(-θ) = secθ

cosec(-θ)= - cosecθII.

sin(90-θ) = cosθ

cos(90-θ) = sinθ

tan(90-θ) = cotθ

cot(90-θ) = tanθ

sec(90-θ) = cosecθ

cosec(90-θ) = secθIII.

sin(90+θ) = cosθ

cos(90+θ) = -sinθ

tan(90+θ) = -cotθ

cot(90+θ) = -tanθ

sec(90+θ) = -cosecθ

cosec(90+θ) = secθIV.

sin(180-θ) = sinθ

cos(180-θ) = -cosθ

tan(180-θ) = -tanθ

cot(180-θ) = cotθ

sec(180-θ) = -secθ

cosec(180-θ) = cosecθV.

sin(180+θ) = -sinθ

cos(180+θ) = -cosθ

tan(180+θ) = tanθ

cot(180+θ) = cotθ

sec(180+θ) = -secθ

cosec(180+θ) = -cosecθ

cot(180-θ)=-cotθ

since cot(180-θ)=1/tan(180-θ)

Where is the supposed "c" in the Left Hand Side?

]]>Bob

]]>Post when you are done and good luck.

]]>1 I would like a formula that would show the answer as either positive or negative depending whether the 2nd cell is lower or higher than the primary cell?

2 I would like the same in another cell to show the difference as a percentage + or - ?

3 Also i would like to know a good place to learn more about Excell formula's?

Thanks

]]>The blue area converges to Gamma.

]]>"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*.