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A multiplication table is an array showing the result of applying a binary operator to elements of a given set S. For example, the following table is the multiplication table ...

A parallelogram is a quadrilateral with opposite sides parallel (and therefore opposite angles equal). A quadrilateral with equal sides is called a rhombus, and a ...

A symmetric polynomial on n variables x_1, ..., x_n (also called a totally symmetric polynomial) is a function that is unchanged by any permutation of its variables. In other ...

Scan the decimal expansion of a constant (including any digits to the left of the decimal point) until all n-digit strings have been seen (including 0-padded strings). The ...

A constant function is function f(x)=c whose value does not change as its parameters vary. The function graph of a one-dimensional constant function is a straight line. The ...

Given a set of linear equations {a_1x+b_1y+c_1z=d_1; a_2x+b_2y+c_2z=d_2; a_3x+b_3y+c_3z=d_3, (1) consider the determinant D=|a_1 b_1 c_1; a_2 b_2 c_2; a_3 b_3 c_3|. (2) Now ...

The cyclic group C_(10) is the unique Abelian group of group order 10 (the other order-10 group being the non-Abelian D_5). Examples include the integers modulo 10 under ...

The cyclic group C_(12) is one of the two Abelian groups of the five groups total of group order 12 (the other order-12 Abelian group being finite group C2×C6). Examples ...

Jordan's lemma shows the value of the integral I=int_(-infty)^inftyf(x)e^(iax)dx (1) along the infinite upper semicircle and with a>0 is 0 for "nice" functions which satisfy ...

Three guests decide to stay the night at a lodge whose rate they are initially told is $30 per night. However, after the guests have each paid $10 and gone to their room, the ...