Consequently, all irrational roots of P have the form -a [+ or -] [e.sub.i][square root of D], i = 1, ..., t, where [e.sub.i] are distinct positive rational numbers
. If P is of odd degree, it has a rational root [alpha].
Elementary school math textbooks in Korea devote far more space to rational number
arithmetic and provide more practice problems than do U.S.
While the solution of the differential equation that is obtained by using the arbitrary values of nonnegative integer n gives the same geodesics as the two-parameter Weibull function, new function that defined nonnegative rational numbers
of n is derived for two-dimensional family of curve.
On the mathematical, cognitive, and instructional foundations of rational numbers
. In A.
(ii) for large values of K and exponent m being a rational number
the formula for S(x) is similar but D(x) takes the form
Transition probabilities of the chain X are clearly rational numbers
so the components of [[pi].sup.(n)], as a solution of a linear system of rational equations, are rational numbers
The other text was Making Sense of Fractions, Ratios, and Proportions (NCTM 2002), the 64th yearbook from the National Council of Teachers of Mathematics (NCTM) that focused specifically on recent research related to issues with rational numbers
and offered us a wider view of the existing research.
Leaving the realm of integers, we remind him as well of the concept of rational number
as a quotient p/q, q[not equal to]0 with integers p and q in lowest terms and known facts such as (i) integers can be considered as rational numbers
, (ii) the decimal expansion of a rational number
always either terminates after finitely many digits or begins to repeat the same finite sequence of digits over and over and again, (iii) any repeating or terminating decimal represents a rational number
Throughout this paper, we use R, [R.sup.+], [R.sup.-], Q, Z, and [Z.sup.+] to denote real numbers, positive real numbers, negative real numbers, rational numbers
, integers, and positive integers, respectively.
Then there exist rational numbers
[[lambda].sub.0], ..., [[lambda].sub.p], not all 0, such that