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The cardinal number of any set is lower than the cardinal number of the set of all its subsets. A corollary is that there is no highest aleph (aleph).

An unhappy number is a number that is not happy, i.e., a number n such that iterating this sum-of-squared-digits map starting with n never reaches the number 1. The first few ...

A factor of a polynomial P(x) of degree n is a polynomial Q(x) of degree less than n which can be multiplied by another polynomial R(x) of degree less than n to yield P(x), ...

An abnormal number is a hypothetical number which can be factored into primes in more than one way. Hardy and Wright (1979) prove the fundamental theorem of arithmetic by ...

A number which does not divide another exactly. For instance, 4 and 5 are aliquant divisors of 6. A number which is not an aliquant divisor (i.e., one that does divide ...

There are several types of numbers that are commonly termed "lucky numbers." The first is the lucky numbers of Euler. The second is obtained by writing out all odd numbers: ...

The negabinary representation of a number n is its representation in base -2 (i.e., base negative 2). It is therefore given by the coefficients a_na_(n-1)...a_1a_0 in n = ...

Iff p is a prime, then (p-1)!+1 is a multiple of p, that is (p-1)!=-1 (mod p). (1) This theorem was proposed by John Wilson and published by Waring (1770), although it was ...

The real part R[z] of a complex number z=x+iy is the real number not multiplying i, so R[x+iy]=x. In terms of z itself, R[z]=1/2(z+z^_), where z^_ is the complex conjugate of ...

A nexus number is a figurate number built up of the nexus of cells less than n steps away from a given cell. The nth d-dimensional nexus number is given by N_d(n) = ...