May 19, 2015 · 5 The definition of an irrational number is that it is not rational. And $0$ is by definition a rational number.

5 I think of the number zero as a whole number. It can certainly be a ratio = $\frac {0} {x}, x \neq 0.$ Therefore it is rational. But any ratio equaling zero involves zero, or is irrational, e.g.$\frac {x} {\infty}, …

Feb 25, 2018 · How to represent 0 as rational number? $0/0$ is not legitimate, $0/\\text{const}$ should be good enough, but what is the right value of const? $0/1$ works for a lot of computational cases, …

$0.333\dots$ is rational because it is expressible as a ratio of two integers. There is nothing more to it. Your claim that it is not a finite ratio is false, and begs the question of why you believe it is not a finite …

Minor point: this is not a proof by contradiction, you prove that qy is irrational by proving that it is not rational, this is just the definition of being irrational.

Sep 15, 2015 · However, if you think about algebraic numbers, which are rational numbers and irrational numbers which can be expressed as roots of polynomials with integer coefficients (like $\sqrt2$ or …

Wikipedia claims that every repeating decimal represents a rational number. According to the following definition, how can we prove that fact? Definition: A number is rational if it can be writt...

Proof: Assume that if a and b are rational numbers, b ≠ 0, and r is an irrational number, then a + br is rational. By the definition of rational, we can substitute a and b with fractions where p, q, m, n are …

Nov 15, 2017 · If f is continuous for every real number and $f (r)=0$ for every rational number, then $f (x)=0$ for all real numbers. Ask Question Asked 8 years, 3 months ago Modified 4 years, 2 months ago

I have been looking at examples showing that the set of all rationals have Lebesgue measure zero. In examples, they always cover the rationals using an infinite number of open intervals, then compu...