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A line is a straight one-dimensional figure having no thickness and extending infinitely in both directions. A line is sometimes called a straight line or, more archaically, ...

For all n, there exists a k such that the kth term of the Goodstein sequence G_k(n)=0. In other words, every Goodstein sequence converges to 0. The secret underlying ...

A non-zero module which is not the direct sum of two of its proper submodules. The negation of indecomposable is, of course, decomposable. An abstract vector space is ...

An ordering for the Cartesian product × of any two sets A and B with order relations <A and <B, respectively, such that if (a_1,b_1) and (a_2,b_2) both belong to A×B, then ...

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 ...

A topology tau on a topological vector space X=(X,tau) (with X usually assumed to be T2) is said to be locally convex if tau admits a local base at 0 consisting of balanced, ...

The Rayleigh functions sigma_n(nu) for n=1, 2, ..., are defined as sigma_n(nu)=sum_(k=1)^inftyj_(nu,k)^(-2n), where +/-j_(nu,k) are the zeros of the Bessel function of the ...

A string of length n on an alphabet l of m characters is an arrangement of n not necessarily distinct symbols from l. There are m^n such distinct strings. For example, the ...

A subset of an algebraic variety which is itself a variety. Every variety is a subvariety of itself; other subvarieties are called proper subvarieties. A sphere of the ...

A recursive function devised by I. Takeuchi in 1978 (Knuth 1998). For integers x, y, and z, it is defined by (1) This can be described more simply by t(x,y,z)={y if x<=y; {z ...