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The Cantor set T_infty, sometimes also called the Cantor comb or no middle third set (Cullen 1968, pp. 78-81), is given by taking the interval [0,1] (set T_0), removing the ...

Let K be a field of arbitrary characteristic. Let v:K->R union {infty} be defined by the following properties: 1. v(x)=infty<=>x=0, 2. v(xy)=v(x)+v(y) forall x,y in K, and 3. ...

A subset {v_1,...,v_k} of a vector space V, with the inner product <,>, is called orthonormal if <v_i,v_j>=0 when i!=j. That is, the vectors are mutually perpendicular. ...

A Smarandache-like function which is defined where S_k(n) is defined as the smallest integer for which n|S_k(n)^k. The Smarandache S_k(n) function can therefore be obtained ...

The term "square" can be used to mean either a square number ("x^2 is the square of x") or a geometric figure consisting of a convex quadrilateral with sides of equal length ...

The area moment of inertia is a property of a two-dimensional plane shape which characterizes its deflection under loading. It is also known as the second moment of area or ...

Let J be a finite group and the image R(J) be a representation which is a homomorphism of J into a permutation group S(X), where S(X) is the group of all permutations of a ...

An interpretation of first-order logic consists of a non-empty domain D and mappings for function and predicate symbols. Every n-place function symbol is mapped to a function ...

An out-shuffle, also known as a perfect shuffle (Golomb 1961), is a riffle shuffle in which the top half of the deck is placed in the right hand, and cards are then ...

If, after constructing a difference table, no clear pattern emerges, turn the paper through an angle of 60 degrees and compute a new table. If necessary, repeat the process. ...