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Let a hotel have a denumerable set of rooms numbered 1, 2, 3, .... Then any finite number n of guests can be accommodated without evicting the current guests by moving the ...

The rook numbers r_k^((m,n)) of an m×n board are the number of subsets of size k such that no two elements have the same first or second coordinate. In other word, it is the ...

The algebraic unknotting number of a knot K in S^3 is defined as the algebraic unknotting number of the S-equivalence class of a Seifert matrix of K. The algebraic unknotting ...

For a particular format in the IEEE 754-2008 framework, a subnormal number is a nonzero floating-point number with magnitude less than the magnitude of that formatÕs smallest ...

A number is said to be cubefree if its prime factorization contains no tripled factors. All primes are therefore trivially cubefree. The cubefree numbers are 1, 2, 3, 4, 5, ...

A semiprime which English economist and logician William Stanley Jevons incorrectly believed no one else would be able to factor. According to Jevons (1874, p. 123), "Can the ...

There are two distinct entities both known as the Lagrange number. The more common one arises in rational approximation theory (Conway and Guy 1996), while the other refers ...

Long multiplication is the method of multiplication that is commonly taught to elementary school students throughout the world. It can be used on two numbers of arbitrarily ...

In 1891, Chebyshev and Sylvester showed that for sufficiently large x, there exists at least one prime number p satisfying x<p<(1+alpha)x, where alpha=0.092.... Since the ...

A totative is a positive integer less than or equal to a number n which is also relatively prime to n, where 1 is counted as being relatively prime to all numbers. The number ...