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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).

A number of the form n^...^_()_(n)n, where Knuth up-arrow notation has been used. The first few Ackermann numbers are 1^1=1, 2^^2=4, and ...

A Moore graph of type (v,g) is a regular graph of vertex degree v>2 and girth g that contains the maximum possible number of nodes, namely ...

A magic square-type arrangement of the words in the Latin sentence "Sator Arepo tenet opera rotas" ("the farmer Arepo keeps the world rolling"). This square has been found in ...

If q_n is the nth prime such that M_(q_n) is a Mersenne prime, then q_n∼(3/2)^n. It was modified by Wagstaff (1983) to yield Wagstaff's conjecture, q_n∼(2^(e^(-gamma)))^n, ...

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 ...

Johnson solid J_(10).

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 ...

Square line picking is the selection of pairs of points (corresponding to endpoints of a line segment) randomly placed inside a square. n random line segments can be picked ...

Consider a combination lock consisting of n buttons that can be pressed in any combination (including multiple buttons at once), but in such a way that each number is pressed ...