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The fifth of Peano's axioms, which states: If a set S of numbers contains zero and also the successor of every number in S, then every number is in S.

The modulus of a complex number z, also called the complex norm, is denoted |z| and defined by |x+iy|=sqrt(x^2+y^2). (1) If z is expressed as a complex exponential (i.e., a ...

The rascal triangle is a number triangle with numbers arranged in staggered rows such that a_(n,r)=n(r-n)+1. (1) The published study of this triangle seems to have originated ...

The number sign # sometimes used in mathematics to indicate the number of a quantity satisfying some condition, e.g., #{n:n>1}. The symbol is also used to denote a primorial.

Given a polygon with an even number of sides, the derived polygon is obtained by joining the points which are a fractional distance r along each side. If r=1/2, then the ...

The Taniyama-Shimura conjecture, since its proof now sometimes known as the modularity theorem, is very general and important conjecture (and now theorem) connecting topology ...

An operation on rings and modules. Given a commutative unit ring R, and a subset S of R, closed under multiplication, such that 1 in S, and 0 not in S, the localization of R ...

A collection of equations satisfies the Hasse principle if, whenever one of the equations has solutions in R and all the Q_p, then the equations have solutions in the ...

If there exists a one-to-one correspondence between two subgroups and subfields such that G(E(G^')) = G^' (1) E(G(E^')) = E^', (2) then E is said to have a Galois theory. A ...

A module is a mathematical object in which things can be added together commutatively by multiplying coefficients and in which most of the rules of manipulating vectors hold. ...