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Negative number. This thermometer is indicating a negative Fahrenheit temperature (−4 °F). In mathematics, a negative number is the opposite (mathematics) of a positive real number. [1] Equivalently, a negative number is a real number that is less than zero. Negative numbers are often used to represent the magnitude of a loss or deficiency.
The Collatz conjecture is: This process will eventually reach the number 1, regardless of which positive integer is chosen initially. That is, for each , there is some with . If the conjecture is false, it can only be because there is some starting number which gives rise to a sequence that does not contain 1.
e. In mathematics, an impossibility theorem is a theorem that demonstrates a problem or general set of problems cannot be solved. These are also known as proofs of impossibility, negative proofs, or negative results. Impossibility theorems often resolve decades or centuries of work spent looking for a solution by proving there is no solution.
Pell's equation. Pell's equation for n = 2 and six of its integer solutions. Pell's equation, also called the Pell–Fermat equation, is any Diophantine equation of the form where n is a given positive nonsquare integer, and integer solutions are sought for x and y. In Cartesian coordinates, the equation is represented by a hyperbola; solutions ...
A finite regular continued fraction, where is a non-negative integer, is an integer, and is a positive integer, for . A continued fraction is a mathematical expression that can be writen as a fraction with a denominator that is a sum that contains another simple or continued fraction. Depending on whether this iteration terminates with a simple ...
Cube root. In mathematics, a cube root of a number x is a number y such that y3 = x. All nonzero real numbers have exactly one real cube root and a pair of complex conjugate cube roots, and all nonzero complex numbers have three distinct complex cube roots. For example, the real cube root of 8, denoted , is 2, because 23 = 8, while the other ...
Solving the inverse relation, as in the previous section, yields the expected 0 i = 1 and −1 i = 0, with negative values of n giving infinite results on the imaginary axis. Plotted in the complex plane , the entire sequence spirals to the limit 0.4383 + 0.3606 i , which could be interpreted as the value where n is infinite.
The real part of log (z) is the natural logarithm of |z|. Its graph is thus obtained by rotating the graph of ln (x) around the z -axis. In mathematics, a complex logarithm is a generalization of the natural logarithm to nonzero complex numbers. The term refers to one of the following, which are strongly related: A complex logarithm of a ...
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