Proof Irrational number x , given N &#x2208;<!-- ∈ --> <mrow class="MJX-TeXAtom-ORD">



Answered question


Proof Irrational number x, given N N exists ϵ > 0 so all rationals V ϵ ( x ) have denominator larger than N.

Answer & Explanation

Jenna Farmer

Jenna Farmer

Beginner2022-07-12Added 17 answers

Since there are only finitely many rational points in [ 0 , 1 ] whose denominator is not larger than N there has to be a ε so small that ( x ε , x + ε ) contains none of them; just take
ε = min { | x y | : y  is rational and its denominator is N } .

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?