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Condition numbers can also be defined for nonlinear functions, and can be computed using calculus.The condition number varies with the point; in some cases one can use the maximum (or supremum) condition number over the domain of the function or domain of the question as an overall condition number, while in other cases the condition number at a particular point is of more interest.
An identity, such as (+) = + +, means that if x is replaced with any number, then the two expressions take the same value. This may also be interpreted as saying that the two sides of the equals sign represent the same function (equality of functions), or that the two expressions denote the same polynomial (equality of polynomials).
In mathematics, the floor function is the function that takes as input a real number x, and gives as output the greatest integer less than or equal to x, denoted ⌊x⌋ or floor(x). Similarly, the ceiling function maps x to the least integer greater than or equal to x, denoted ⌈x⌉ or ceil(x). [1]
In mathematics, the complex conjugate of a complex number is the number with an equal real part, and an imaginary part equal in magnitude but opposite in sign. That is, if a {\displaystyle a} and b {\displaystyle b} are real numbers, then the complex conjugate of a + b i {\displaystyle a+bi} is a − b i . {\displaystyle a-bi.}
In languages such as C, relational operators return the integers 0 or 1, where 0 stands for false and any non-zero value stands for true. An expression created using a relational operator forms what is termed a relational expression or a condition .
Value Notes Any 1 0… NaR: anything not mathematically definable as a unique real number [9] Any 0 0… 0: Any 0 10… 1: Any 1 10… −1: Any 0 0 1 11 0… 0.5: Any 0 0… 1 + smallest positive value Any 0 1… largest positive value posit8 0 000000 1
The binary number system expresses any number as a sum of powers of 2, and denotes it as a sequence of 0 and 1, separated by a binary point, where 1 indicates a power of 2 that appears in the sum; the exponent is determined by the place of this 1: the nonnegative exponents are the rank of the 1 on the left of the point (starting from 0), and ...