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It was common into the 18th century to use an abbreviation of the word equals as the symbol for equality; examples included æ and œ , from the Latin aequālis. [10] Diophantus's use of ἴσ , short for ἴσος (ísos 'equals'), in Arithmetica (c. 250 AD) is considered one of the first uses of an equals sign. [11]
For example, π(10) = 4 because there are four prime numbers (2, 3, 5 and 7) less than or equal to 10. The prime number theorem then states that x / log x is a good approximation to π ( x ) (where log here means the natural logarithm), in the sense that the limit of the quotient of the two functions π ( x ) and x / log x as x increases ...
may mean that A is a subset of B, and is possibly equal to B; that is, every element of A belongs to B; expressed as a formula, ,. 2. A ⊂ B {\displaystyle A\subset B} may mean that A is a proper subset of B , that is the two sets are different, and every element of A belongs to B ; expressed as a formula, A ≠ B ∧ ∀ x , x ∈ A ⇒ x ∈ ...
It is the second Fibonacci prime (and the second Lucas prime), the second Sophie Germain prime, the third Harshad number in base 10, and the second factorial prime, as it is equal to 2! + 1. 3 is the second and only prime triangular number, [5] and Gauss proved that every integer is the sum of at most 3 triangular numbers.
The final digit of a triangular number is 0, 1, 3, 5, 6, or 8, and thus such numbers never end in 2, 4, 7, or 9. A final 3 must be preceded by a 0 or 5; a final 8 must be preceded by a 2 or 7. In base 10, the digital root of a nonzero triangular number is always 1, 3, 6, or 9. Hence, every triangular number is either divisible by three or has a ...
The equals sign (British English) or equal sign (American English), also known as the equality sign, is the mathematical symbol =, which is used to indicate equality in some well-defined sense. [1] In an equation, it is placed between two expressions that have the same value, or for which one studies the conditions under which they have the ...
For example, 3 is a divisor of 21, since 21/7 = 3 (and therefore 7 is also a divisor of 21). ... a perfect number equals the sum of its proper divisors; ...
Every equal-interval number (e.g. 123, 135, 753) duplicated to a palindrome (e.g. 123321, 753357) renders a multiple of both 11 and 111 (3 × 37 in decimal). In decimal 37 is a permutable prime with 73, which is the twenty-first prime number. By extension, the mirroring of their digits and prime indexes makes 73 the only Sheldon prime.