64 (number) it is possible to find sequences of 64 consecutive integers such that each inner member shares a factor with either the first or the last member, 64 is an Erdős–Woods number. In base 10, no integer added up to its own digits yields 64, hence it is a self number. 64 is a superperfect number—a number such that σ(σ("n")) = 2"n". 64 is the index of Graham's number in the rapidly growing sequence 3↑↑↑↑3, 3 ↑ 3,… Sixty-four is: 64 (number) 64 (sixty-four) is the natural number following 63 and preceding 65. Sixty-four is the square of 8, the cube
Proof that e is irrational and "b" such that "e" = ⁄. Define the number To see that if "e" is rational, then "x" is an integer, substitute "e" = ⁄ into this definition to obtain The first term is an integer, and every fraction in the sum is actually an integer because "n" ≤ "b" for each term. Therefore, "x" is an integer. We now prove that . First, to prove that "x" is strictly positive, we insert the above series representation of "e" into the definition of "x" and obtain because all the terms are strictly positive. We now prove that "x" <