Question

show that q set of rational numbers is not a complete field. ​

Answer 1

Answer:

Let x be an irrational number , then take two rational sequences an and bn (rational sequences means that every term of that sequence is a rational number) such that both of them converge to x and an is less than or equal to bn for every natural n.

Then it's easy to show that sup(an)=inf(bn)=x but yet x is not a rational number therefore the set of rational numbers is not an order complete field.