Search results
Results From The WOW.Com Content Network
For example, a loop that iterates five times (from 0 to 4 inclusive) can be written as a half-open interval from 0 to 5: for ( index = 0 ; index < 5 ; index ++ ) { /* Body of the loop */ } The loop body is executed first of all with index equal to 0; index then becomes 1, 2, 3, and finally 4 on successive iterations.
Freivalds' algorithm utilizes randomization in order to reduce this time bound to () [2] with high probability. In O ( k n 2 ) {\displaystyle O(kn^{2})} time the algorithm can verify a matrix product with probability of failure less than 2 − k {\displaystyle 2^{-k}} .
Zero to the power of zero, denoted as 0 0, is a mathematical expression that can take different values depending on the context. In certain areas of mathematics, such as combinatorics and algebra, 0 0 is conventionally defined as 1 because this assignment simplifies many formulas and ensures consistency in operations involving exponents.
For example, using single-precision IEEE arithmetic, if x = −2 −149, then x/2 underflows to −0, and dividing 1 by this result produces 1/(x/2) = −∞. The exact result −2 150 is too large to represent as a single-precision number, so an infinity of the same sign is used instead to indicate overflow.
Signum function = . In mathematics, the sign function or signum function (from signum, Latin for "sign") is a function that has the value −1, +1 or 0 according to whether the sign of a given real number is positive or negative, or the given number is itself zero.
In some mathematical contexts, zero-based numbering can be used without confusion, when ordinal forms have well established meaning with an obvious candidate to come before first; for instance, a zeroth derivative of a function is the function itself, obtained by differentiating zero times. Such usage corresponds to naming an element not ...
The same formula applies to octonions, with a zero real part and a norm equal to 1. These formulas are a direct generalization of Euler's identity, since i {\displaystyle i} and − i {\displaystyle -i} are the only complex numbers with a zero real part and a norm (absolute value) equal to 1.
Example of Kleene plus applied to the empty set: ∅ + = ∅ ∅ * = { } = ∅, where concatenation is an associative and noncommutative product. Example of Kleene plus and Kleene star applied to the singleton set containing the empty string: