Question

Which of the following is not a subset of the set of rational numbers? (Points : 1)
Natural Numbers
Integers
Whole Numbers
Real Numbers

Answer 1

what defines a number as ratioanl?

Answer 2

Rational Number Can Be Written As A Fraction

Answer 3

Note that \(X \subset Y\) if for every \(x \in X\) we have \(x \in Y\).

Answer 4

"as a fraction" is close ... but it requires a little more care.\[\frac{\sqrt{2}}{3}\]is written like a fraction, but it is not a ratioanl number

Answer 5

the top and bottom of the "fraction" have to be expressed as integers

Answer 6

The precise definition is any number of the form \(\frac{p}{q}\) with \(p, q \in \mathbb{Z}\) and \(q \neq 0\)

Answer 7

the top 3 options all consist of integers, and can be written in a rational form.

can you think of a real number that cannot be written "like a fraction"?

Answer 8

Is there an a number \(x\) in the set of real numbers which is not rational? Is there an \(x \in \mathbb{R}\) such that \(x \not\in \mathbb{Q}\)?