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Transfinite induction, like regular induction, is used to show a property P(n) holds for all numbers n. The essential difference is that regular induction is restricted to ...

Let F_n be the nth Fibonacci number, and let (p|5) be a Legendre symbol so that e_p=(p/5)={1 for p=1,4 (mod 5); -1 for p=2,3 (mod 5). (1) A prime p is called a Wall-Sun-Sun ...

A Wieferich prime is a prime p which is a solution to the congruence equation 2^(p-1)=1 (mod p^2). (1) Note the similarity of this expression to the special case of Fermat's ...

The q-analog of the derivative, defined by (d/(dx))_qf(x)=(f(x)-f(qx))/(x-qx). (1) For example, (d/(dx))_qsinx = (sinx-sin(qx))/(x-qx) (2) (d/(dx))_qlnx = ...

The Werner formulas are the trigonometric product formulas 2sinalphacosbeta = sin(alpha-beta)+sin(alpha+beta) (1) 2cosalphacosbeta = cos(alpha-beta)+cos(alpha+beta) (2) ...

The prime number theorem gives an asymptotic form for the prime counting function pi(n), which counts the number of primes less than some integer n. Legendre (1808) suggested ...

The study of angles and of the angular relationships of planar and three-dimensional figures is known as trigonometry. The trigonometric functions (also called the circular ...

One of the ranges into which data in a frequency distribution table (or histogram) are binned. The ends of a class interval are called class limits, and the middle of an ...

The average of the values of the class limits for a given class. A class mark is also called a midvalue or central value (Kenney and Keeping 1962, p. 14), and is commonly ...

If f(x) is positive and decreases to 0, then an Euler constant gamma_f=lim_(n->infty)[sum_(k=1)^nf(k)-int_1^nf(x)dx] can be defined. For example, if f(x)=1/x, then ...