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For a linear homogeneous ordinary differential equation, if y_1(x) and y_2(x) are solutions, then so is y_1(x)+y_2(x).

A syllogism, also known as a rule of inference, is a formal logical scheme used to draw a conclusion from a set of premises. An example of a syllogism is modus ponens.

Let rho be a reciprocal difference. Then Thiele's interpolation formula is the continued fraction f(x)=f(x_1)+(x-x_1)/(rho(x_1,x_2)+)(x-x_2)/(rho_2(x_1,x_2,x_3)-f(x_1)+) ...

Every real number is negative, 0, or positive. The law is sometimes stated as "For arbitrary real numbers a and b, exactly one of the relations a<b, a=b, a>b holds" (Apostol ...

Given a nonhomogeneous ordinary differential equation, select a differential operator which will annihilate the right side, and apply it to both sides. Find the solution to ...

An ungula is a portion of a solid of revolution obtained by cutting via a plane oblique to its base. The term derives from the Latin word ungula for the hoof of a horse. ...

A universal sentence is a sentence (i.e., formula of the predicate calculus without free variables) whose variables are universally quantified.

A set of three conjectures proposed by Weil in 1942 for extending Riemann hypothesis-like statements to classes of mathematical structures. The conjectures were proved by ...

Every nonempty set of positive integers contains a smallest member.

The probability law on the space of continuous functions g with g(0)=0, induced by the Wiener process.