## Related questions with answers

Question

Is this statement true or false? Explain your answer. $\forall$ real numbers $x \exists$ an integer $n$ such that $n x$ is an integer.

Solution

VerifiedAnswered 2 years ago

Answered 2 years ago

Step 1

1 of 2$\displaystyle \begin{array}{ c c } \boxed{\mathrm{False.}} & \mathrm{Suppose} \ x\ =\ \pi \ \mathrm{and} \ n\ =\ 3.\ \mathrm{Then} \ nx\ =\ 3\pi \ =\mathrm{which\ is\ not\ an\ integer.} \ \end{array}$

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