Since ([K.sub.X], [gamma]) < 0 and ([E.sub.n], [gamma]) > 0, there exists a unique positive

rational number [b.sub.n] such that ([K.sub.X] + [b.sub.n][E.sub.n], [gamma]) = 0 for any n [greater than or equal to] 0.

Alas, transcendental numbers can be approximated exceptionally well by

rational numbers, because their continued fractions contain large denominators and can be truncated with minimum loss of precision.

Although there are inherent difficulties in working with

rational numbers, there also are cultural sources of difficulty, according to an article in Psychology Today.

On the mathematical, cognitive, and instructional foundations of

rational numbers. In A.

La otra, desde una perspectiva cognitiva, destaca el trabajo de Thomas Kieren sobre los procesos de aprendizaje de los numeros racionales basados en su nocion de constructo matematico, y The

Rational Number Project coordinado por Merlyn J.

On the other hand, we prove in Proposition 7 that, surprisingly enough,

rational numbers are not computable (except for a few explicitly exhibited ones).

Initial fraction learning by fourth- and fifth-grade students: A comparison of the effects of using commercial curricula with the effects of using the

Rational Number Project curriculum.

Order and equivalence of

rational numbers: A clinical teaching experiment.

Is [square root of 2] a

rational number, that is, expressible as a fraction?

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.

A Kronrod rule also has a Jacobi matrix, in which the numbers [a.sub.k] and [b.sub.k] are

rational numbers that can be found by the process described in [10].

The

rational number constructs: Its elements and mechanisms.