Representing numbers: prime and irrational
نویسنده
چکیده
This article draws an analogy between prime and irrational numbers with respect to how these numbers are defined and how they are perceived by learners. Excerpts are presented from two research studies: a study on understanding prime numbers by pre-service elementary school teachers and a study on understanding irrational numbers by pre-service secondary school teachers. Considering the results of these studies, the author calls for further attention in teaching to transparent features in representation of numbers and suggests several strategies on how this may be achieved.
منابع مشابه
An extension of the mixed integer part of a nonlinear form
Our aim in this paper is to consider the integer part of a nonlinear form representing primes. We establish that if [Formula: see text] are positive real numbers, at least one of the ratios [Formula: see text] ([Formula: see text]) is irrational, then the integer parts of [Formula: see text] are prime infinitely often for [Formula: see text], where [Formula: see text] are natural numbers.
متن کاملIrrationality of E
For simplicity, we follow the rules: k, n, p, K, N are natural numbers, x, y, e1 are real numbers, s1, s2, s3 are sequences of real numbers, and s4 is a finite sequence of elements of R. Let us consider x. We introduce x is irrational as an antonym of x is rational. Let us consider x, y. We introduce x as a synonym of x. One can prove the following two propositions: (1) If p is prime, then √ p ...
متن کاملZero-Tolerance Math: A Defense of “No Math”
In this paper I extend the concept of “No Math” which was first introduced by Harris (2000) during the Florida elections. The results of this work show the existence of a hitherto unknown class of numbers, dubbed politically correct numbers. It is also shown that all other numbers are either illegal or irrational, and should therefore not be taught to children. The “zero-tolerance” math develop...
متن کاملOn Sums of Primes from Beatty Sequences
Ever since the days of Euler and Goldbach, number-theorists have been fascinated by additive representations of the integers as sums of primes. The most famous result in this field is I.M. Vinogradov’s three primes theorem [7], which states that every sufficiently large odd integer is the sum of three primes. Over the years, a number of authors have studied variants of the three primes theorem ...
متن کاملDiophantine Approximation by Cubes of Primes and an Almost Prime II
Let λ1, . . . , λ4 be non-zero with λ1/λ2 irrational and negative, and let S be the set of values attained by the form λ1x 3 1 + · · · + λ4x4 when x1 has at most 3 prime divisors and the remaining variables are prime. We prove that most real numbers are close to an element of S.
متن کامل