- published: 29 May 2014
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40 (forty) is the natural number following 39 and preceding 41.
Despite being related to the word "four" (4), 40 is spelled "forty", and not "fourty". The reason is that etymologically (also in accents without the horse–hoarse merger), the words have different vowels, "forty" containing a contraction in the same way that "fifty" contains a contraction of "five".
Forty is an octagonal number, and as the sum of the first four pentagonal numbers, it is a pentagonal pyramidal number. Adding up some subsets of its divisors (e.g., 1, 4, 5, 10 and 20) gives 40, hence 40 is a semiperfect number.
Given 40, the Mertens function returns 0. 40 is the smallest number n with exactly 9 solutions to the equation φ(x) = n.
Forty is the number of n-queens problem solutions for n = 7.
Since 402 + 1 = 1601 is prime, 40 is a Størmer number.
40 is a repdigit in base 3 (1111) and a Harshad number in base 10.
The number 40 is significant in Jewish, Christian, Islamic, and other Middle Eastern traditions. It can represent an estimate, or many of something.
A number is a mathematical object used to count and measure. In mathematics, the definition of number has been extended over the years to include such numbers as zero, negative numbers, rational numbers, irrational numbers, and complex numbers.
Mathematical operations are certain procedures that take one or more numbers as input and produce a number as output. Unary operations take a single input number and produce a single output number. For example, the successor operation adds one to an integer, thus the successor of 4 is 5. Binary operations take two input numbers and produce a single output number. Examples of binary operations include addition, subtraction, multiplication, division, and exponentiation. The study of numerical operations is called arithmetic.
A notational symbol that represents a number is called a numeral. In addition to their use in counting and measuring, numerals are often used for labels (telephone numbers), for ordering (serial numbers), and for codes (e.g., ISBNs).
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