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Excel maintains 15 figures in its numbers, but they are not always accurate; mathematically, the bottom line should be the same as the top line, in 'fp-math' the step '1 + 1/9000' leads to a rounding up as the first bit of the 14 bit tail '10111000110010' of the mantissa falling off the table when adding 1 is a '1', this up-rounding is not undone when subtracting the 1 again, since there is no ...
However, f (x) is not the zero function, so does not equal its Taylor series around the origin. Thus, f (x) is an example of a non-analytic smooth function. In real analysis, this example shows that there are infinitely differentiable functions f (x) whose Taylor series are not equal to f (x) even if they converge.
The second term after the equal sign is the omitted-variable bias in this case, which is non-zero if the omitted variable z is correlated with any of the included variables in the matrix X (that is, if X′Z does not equal a vector of zeroes). Note that the bias is equal to the weighted portion of z i which is "explained" by x i.
In statistics, the bias of an estimator (or bias function) is the difference between this estimator's expected value and the true value of the parameter being estimated. An estimator or decision rule with zero bias is called unbiased. In statistics, "bias" is an objective property of an estimator.
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 numerical analysis, a root-finding algorithm is an algorithm for finding zeros, also called "roots", of continuous functions. A zero of a function f is a number x such that f(x) = 0. As, generally, the zeros of a function cannot be computed exactly nor expressed in closed form, root-finding
The ring of 2×2 matrices with integer entries does not satisfy the zero-product property: if = and = (), then = () = =, yet neither nor is zero. The ring of all functions: [,], from the unit interval to the real numbers, has nontrivial zero divisors: there are pairs of functions which are not identically equal to zero yet whose product is the ...
What appears to the modern reader as the representing function's logical inversion, i.e. the representing function is 0 when the function R is "true" or satisfied", plays a useful role in Kleene's definition of the logical functions OR, AND, and IMPLY, [2]: 228 the bounded-[2]: 228 and unbounded-[2]: 279 ff mu operators and the CASE function.