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An unsolvable problem in logic dating back to the ancient Greeks and quoted, for example, by German philosopher Carl von Prantl (1855). The dilemma consists of a crocodile ...

A metatheorem in mathematical logic also known under the name "conditional proof." It states that if the sentential formula B can be derived from the set of sentential ...

A dot plot, also called a dot chart, is a type of simple histogram-like chart used in statistics for relatively small data sets where values fall into a number of discrete ...

A fibered category F over a topological space X consists of 1. a category F(U) for each open subset U subset= X, 2. a functor i^*:F(U)->F(V) for each inclusion i:V↪U, and 3. ...

One of the beautiful arrangements of circles found at the Temple of Osiris at Abydos, Egypt (Rawles 1997). The pattern also appears in Phoenician art from the 9th century BC ...

In mathematics, a formula is a fact, rule, or principle that is expressed in terms of mathematical symbols. Examples of formulas include equations, equalities, identities, ...

The great rhombic triacontahedron, also called the great stellated triacontahedron, is the dual of great icosidodecahedron uniform polyhedron. It is a zonohedron and a ...

There are two important theorems known as Herbrand's theorem. The first arises in ring theory. Let an ideal class be in A if it contains an ideal whose lth power is ...

The grouping of data into bins (spaced apart by the so-called class interval) plotting the number of members in each bin versus the bin number. The above histogram shows the ...

Given a short exact sequence of modules 0->A->B->C->0, (1) let ...->P_2->^(d_2)P_1->^(d_1)P_0->^(d_0)A->0 (2) ...->Q_2->^(f_2)Q_1->^(f_1)Q_0->^(f_0)C->0 (3) be projective ...