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The axis in the complex plane corresponding to zero real part, R[z]=0.

An imaginary quadratic field is a quadratic field Q(sqrt(D)) with D<0. Special cases are summarized in the following table. D field members -1 Gaussian integer -3 Eisenstein ...

The imaginary number i=sqrt(-1), i.e., the square root of -1. The imaginary unit is denoted and commonly referred to as "i." Although there are two possible square roots of ...

A game in which the possible moves are the same for each player in any position. All positions in all impartial games form an additive Abelian group. For impartial games in ...

A function which is not defined explicitly, but rather is defined in terms of an algebraic relationship (which can not, in general, be "solved" for the function in question). ...

Given F_1(x,y,z,u,v,w) = 0 (1) F_2(x,y,z,u,v,w) = 0 (2) F_3(x,y,z,u,v,w) = 0, (3) if the determinantof the Jacobian |JF(u,v,w)|=|(partial(F_1,F_2,F_3))/(partial(u,v,w))|!=0, ...

Three impossible ways to combine four bars.

An impossible figure that locally (but only locally!) looks like a torus.

A fraction p/q>=1. A fraction with p/q<1 is called a proper fraction. Therefore, the special cases 1/1, 2/2, 3/3, etc. are generally considered to be improper.

The subset consisting of all elements of a given set is called an improper subset (Kamke 1950, p. 6).