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Two quantities are said to be different (or "unequal") if they are not equal. The term "different" also has a technical usage related to modules. Let a module M in an ...

int_0^pi(sin[(n+1/2)x])/(2sin(1/2x))dx=1/2pi, where the integral kernel is the Dirichlet kernel.

A generalization by Kronecker of Kummer's theory of prime ideal factors. A divisor on a full subcategory C of mod(A) is an additive mapping chi on C with values in a ...

The set of all edge automorphisms of G, denoted Aut^*(G). Let L(G) be the line graph of a graph G. Then the edge automorphism group Aut^*(G) is isomorphic to Aut(L(G)), ...

A proof which can be accomplished using only real numbers (i.e., real analysis instead of complex analysis; Hoffman 1998, pp. 92-93).

delta(r)=sqrt(r)-2alpha(r), where alpha(r) is the elliptic alpha function.

A proof of a formula on limits based on the epsilon-delta definition. An example is the following proof that every linear function f(x)=ax+b (a,b in R,a!=0) is continuous at ...

Two matrices A and B are equal to each other, written A=B, if they have the same dimensions m×n and the same elements a_(ij)=b_(ij) for i=1, ..., n and j=1, ..., m. ...

The series sumf(n) for a monotonic nonincreasing f(x) is convergent if lim_(x->infty)^_(e^xf(e^x))/(f(x))<1 and divergent if lim_(x->infty)__(e^xf(e^x))/(f(x))>1.

A more common way to describe a Euclidean ring.