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A clear-cut way of describing every object in a class in a one-to-one manner.

A one-dimensional geometric object such as a pencil or line segment range.

A 1-form omega=sum_(i=1)^na_i(x)dx_i such that omega=0.

An expression built up from statements letters by appropriate application of connectives (Mendelson 1997, p. 13).

A 1-form w is said to be exact in a region R if there is a function f that is defined and of class C^1 (i.e., is once continuously differentiable in R) and such that df=w.

Consider the forms Q for which the generic characters chi_i(Q) are equal to some preassigned array of signs e_i=1 or -1, e_1,e_2,...,e_r, subject to product_(i=1)^(r)e_i=1. ...

The modular equation of degree five can be written (u/v)^3+(v/u)^3=2(u^2v^2-1/(u^2v^2)).

All elementary functions can be extended to the complex plane. Such definitions agree with the real definitions on the x-axis and constitute an analytic continuation.

Let A be a matrix with the elementary divisors of its characteristic matrix expressed as powers of its irreducible polynomials in the field F[lambda], and consider an ...

If x_0 is an ordinary point of the ordinary differential equation, expand y in a Taylor series about x_0. Commonly, the expansion point can be taken as x_0=0, resulting in ...