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The series for the inverse tangent, tan^(-1)x=x-1/3x^3+1/5x^5+.... Plugging in x=1 gives Gregory's formula 1/4pi=1-1/3+1/5-1/7+1/9-.... This series is intimately connected ...

Let A be a relational system, and let L be a language which is appropriate for A. Let phi be a well-formed formula of L, and let s be a valuation in A. Then A|=_sphi is ...

Let the values of a function f(x) be tabulated at points x_i equally spaced by h=x_(i+1)-x_i, so f_1=f(x_1), f_2=f(x_2), .... Then Weddle's rule approximating the integral of ...

The symbol O(x), pronounced "big-O of x," is one of the Landau symbols and is used to symbolically express the asymptotic behavior of a given function. In particular, if n is ...

A number x is said to have "n figures" if it takes n digits to express it. The number of figures is therefore equal to one more than the power of 10 in the scientific ...

If u_n>0 and given B(n) a bounded function of n as n->infty, express the ratio of successive terms as |(u_n)/(u_(n+1))|=1+h/n+(B(n))/(n^r) for r>1. The series converges for ...

The symbol o(x), pronounced "little-O of x," is one of the Landau symbols and is used to symbolically express the asymptotic behavior of a given function. In particular, if n ...

When a number is expressed in scientific notation, the number of significant digits (or significant figures) is the number of digits needed to express the number to within ...

A proof that is only based on visual elements, without any comments. An arithmetic identity can be demonstrated by a picture showing a self-evident equality between numerical ...

Consider a clause (disjunction of literals) obtained from those of a first-order logic formula Phi in Skolemized form forall x_1... forall x_nS. Then an atomic statement ...