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The silver ratio is a Pisot–Vijayaraghavan number (PV number), as its conjugate 1 − √ 2 = −1 / δ S ≈ −0.41421 has absolute value less than 1. In fact it is the second smallest quadratic PV number after the golden ratio. This means the distance from δ n S to the nearest integer is 1 / δ n S ≈ 0.41421 n.
Cross-multiplication. In mathematics, specifically in elementary arithmetic and elementary algebra, given an equation between two fractions or rational expressions, one can cross-multiply to simplify the equation or determine the value of a variable. The method is also occasionally known as the "cross your heart" method because lines resembling ...
For example, taking the statement x + 1 = 0, if x is substituted with 1, this implies 1 + 1 = 2 = 0, which is false, which implies that if x + 1 = 0 then x cannot be 1. If x and y are integers, rationals, or real numbers, then xy = 0 implies x = 0 or y = 0. Consider abc = 0. Then, substituting a for x and bc for y, we learn a = 0 or bc = 0.
In mathematics and computer programming, the order of operations is a collection of rules that reflect conventions about which operations to perform first in order to evaluate a given mathematical expression. These rules are formalized with a ranking of the operations. The rank of an operation is called its precedence, and an operation with a ...
The metallic mean (also metallic ratio, metallic constant, or noble means[1]) of a natural number n is a positive real number, denoted here that satisfies the following equivalent characterizations: the unique positive real number such that. the positive root of the quadratic equation. the number.
Product of two numbers. Originally, a product was and is still the result of the multiplication of two or more numbers. For example, 15 is the product of 3 and 5. The fundamental theorem of arithmetic states that every composite number is a product of prime numbers, that is unique up to the order of the factors.
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The Cartesian square of a set X is the Cartesian product X2 = X × X. An example is the 2-dimensional plane R2 = R × R where R is the set of real numbers: [1] R2 is the set of all points (x,y) where x and y are real numbers (see the Cartesian coordinate system). The n-ary Cartesian power of a set X, denoted.