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The number of real roots of an algebraic equation with real coefficients whose real roots are simple over an interval, the endpoints of which are not roots, is equal to the ...

Let sigma_0(n) and sigma_1(n) denote the number and sum of the divisors of n, respectively (i.e., the zeroth- and first-order divisor functions). A number n is called sublime ...

The minimal polynomial S_n(x) whose roots are sums and differences of the square roots of the first n primes, ...

Given any two distinct points x,y, there exist neighborhoods u and v of x and y, respectively, with u intersection v=emptyset. It then follows that finite subsets are closed.

Two curves both containing the point P are tangent at P if they share the same tangent line at P.

A number of attractive 60-compounds of the regular tetrahedron can be constructed. The compound illustrated above will be implemented in a future version of the Wolfram ...

A topological basis is a subset B of a set T in which all other open sets can be written as unions or finite intersections of B. For the real numbers, the set of all open ...

One of Cantor's ordinal numbers omega, omega+1, omega+2, ..., omega+omega, omega+omega+1, ... which is "larger" than any whole number.

The function psi(x)={x(1-(x^2)/(c^2))^2 for |x|<c; 0 for |x|>c (1) sometimes used in robust estimation. It has a minimum at x=-c/sqrt(5) and a maximum at x=c/sqrt(5), where ...

The point in the plane with Cartesian coordinates (1, 1).