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

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, …

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}, …

Jun 27, 2020 · I am just curious if 0 is a real number. The definition of a real number is all rational and irrational numbers. And the def definition for rational number is that "$\mathbb {Q}= {a\div b|a,b\in\

Jul 28, 2015 · $1/3=0.333333$ Here $3$ is recurring , so from statement 1) $0.3333$ or $1/3$ is a rational number. And also $0.3333$ is non-terminating as the decimal is not ending or the remainder …

$0.333\dots$ 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 …

Aug 3, 2012 · I know that division by zero is undefined and is also not rational, but I am not sure whether this means it's irrational because it is undefined. Can anyone clarify?

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.

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...

Apr 11, 2020 · Prove the following: The product of a nonzero rational number and an irrational number is also irrational. I assumed the following: Let $r = c/d$ be rational, where $c$ and $d$ are integers and …