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The set of all points x that can be put into one-to-one correspondence with sets of essentially distinct values of four homogeneous coordinates x_0:x_1:x_2:x_3, not all ...

A totally disconnected space is a space in which all subsets with more than one element are disconnected. In particular, if it has more than one element, it is a disconnected ...

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 ...

A projection of a link is tricolorable if each of the strands in the projection can be colored in one of three different colors such that, at each crossing, all three colors ...

The roots (sometimes also called "zeros") of an equation f(x)=0 are the values of x for which the equation is satisfied. Roots x which belong to certain sets are usually ...

A complete set of mutually conjugate group elements. Each element in a group belongs to exactly one class, and the identity element (I=1) is always in its own class. The ...

The cross polytope beta_n is the regular polytope in n dimensions corresponding to the convex hull of the points formed by permuting the coordinates (+/-1, 0, 0, ..., 0). A ...

Given a real m×n matrix A, there are four associated vector subspaces which are known colloquially as its fundamental subspaces, namely the column spaces and the null spaces ...

Let two players each have a finite number of pennies (say, n_1 for player one and n_2 for player two). Now, flip one of the pennies (from either player), with each player ...

In a rectangular room (a cuboid) with dimensions 30^'×12^'×12^', a spider is located in the middle of one 12^'×12^' wall one foot away from the ceiling. A fly is in the ...