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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]
y = x 3 for values of 1 ≤ x ≤ 25. In arithmetic and algebra, the cube of a number n is its third power, that is, the result of multiplying three instances of n together. The cube of a number or any other mathematical expression is denoted by a superscript 3, for example 2 3 = 8 or (x + 1) 3. The cube is also the number multiplied by its square:
Algebra is the branch of mathematics that studies certain abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic operations other than the standard arithmetic operations, such as addition and multiplication.
For example, the third triangular number is (3 × 2 =) 6, the seventh is (7 × 4 =) 28, the 31st is (31 × 16 =) 496, and the 127th is (127 × 64 =) 8128. 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 mathematics, an equation is a mathematical formula that expresses the equality of two expressions, by connecting them with the equals sign =. [2] [3] The word equation and its cognates in other languages may have subtly different meanings; for example, in French an équation is defined as containing one or more variables, while in English ...
This form is sometimes used to prevent falsifying a 3 as an 8. ... as it is equal to 2! + 1. 3 is the second and only prime triangular ... 18 19 20 3 x: 3: 9 27 81: ...
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In mathematics, a product is the result of multiplication, or an expression that identifies objects (numbers or variables) to be multiplied, called factors.For example, 21 is the product of 3 and 7 (the result of multiplication), and (+) is the product of and (+) (indicating that the two factors should be multiplied together).