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For every partition of all the points on a line into two nonempty sets such that no point of either lies between two points of the other, there is a point of one set which ...

The points on a line can be put into a one-to-one correspondence with the real numbers.

In common usage, a cardinal number is a number used in counting (a counting number), such as 1, 2, 3, .... In formal set theory, a cardinal number (also called "the ...

A sequence a_1, a_2, ... such that the metric d(a_m,a_n) satisfies lim_(min(m,n)->infty)d(a_m,a_n)=0. Cauchy sequences in the rationals do not necessarily converge, but they ...

Number Theory

An odd alternating permutation number, more commonly called an Euler number or secant number.

An even alternating permutation number, more commonly called a tangent number.

The algebraic integers in a number field.

A number n is called a k e-perfect number if sigma_e(n)=kn, where sigma_e(n) is the sum of the e-divisors of n.

A number n for which a shortest chain exists (which is also a Hansen chain) is called a Hansen number.