Prove: In every interval there is a rational and an

Gabriella Sellers

Gabriella Sellers

Answered question

2022-06-23

Prove: In every interval there is a rational and an irrational number.

Answer & Explanation

ejigaboo8y

ejigaboo8y

Beginner2022-06-24Added 29 answers

Supposing you mean an interval ( x , y ) of length y x = l > 0 (it doesn't matter whether l is rational or irrational), you can simply choose any integer n > 1 l , and then the interval will contain a rational number of the form a n with a Z . Indeed if a is the largest integer such that a n x (which is well defined) then a = a + 1 will do. By choosing n > 2 l you even get two rationals of this form, and an irrational number between those two by an argument you claim to already have.

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