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An algebraic function is a function f(x) which satisfies p(x,f(x))=0, where p(x,y) is a polynomial in x and y with integer coefficients. Functions that can be constructed ...

Any bounded planar region with positive area >A placed in any position of the unit square lattice can be translated so that the number of lattice points inside the region ...

Let the absolute frequencies of occurrence of an event in a number of class intervals be denoted f_1, f_2, .... The cumulative frequency corresponding to the upper boundary ...

A finitely presented group is a group with a finite number of generators and relations. A mathematical joke involving finitely presented groups is given by Renteln and Dundes ...

Let S be a nonempty set of real numbers that has a lower bound. A number c is the called the greatest lower bound (or the infimum, denoted infS) for S iff it satisfies the ...

Hackenbush is a game in combinatorial game theory in which player Left can delete any bLue edge, player Right can delete any Red edge, and either player can delete Green ...

Let a_n>=0 and suppose sum_(n=1)^inftya_ne^(-an)∼1/a as a->0^+. Then sum_(n<=x)a_n∼x as x->infty. This theorem is a step in the proof of the prime number theorem, but has ...

Let {f_n(x)} be a sequence of analytic functions regular in a region G, and let this sequence be uniformly convergent in every closed subset of G. If the analytic function ...

There are 432 enantiomorphous and 415 chiral fully supported stellations of the icosidodecahedron. Using Miller's rules gives 7071672 enantiomorphous stellations and an ...

Let S be a nonempty set of real numbers that has an upper bound. Then a number c is called the least upper bound (or the supremum, denoted supS) for S iff it satisfies the ...