Let q be irrational. Let a,b be rationals such that a<q<b. If there exists an element p s.t. a<p<b, would it be valid to conclude q=p?

piopiopioirp

piopiopioirp

Answered question

2022-11-14

Let q be irrational. Let a , b be rationals such that a < q < b. If there exists an element p s.t. a < p < b, would it be valid to conclude q = p?

Answer & Explanation

trivialaxxf

trivialaxxf

Beginner2022-11-15Added 21 answers

You certainly cannot conclude that p = q. In fact a < 1 2 ( a + b ) < b and (since you said q is irrational) q 1 2 ( a + b ). Also, either q + 1 2 ( b a ) or q 1 2 ( b a ) will be another irrational between a and b.

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