Exercise 1.4.4

We must show the two conditions for a least upper bound

(i)

Clearly $t\le b$ for all $t\in T$

(ii)

Let $a<b^{\prime }<b$. $b^{\prime }$ Cannot be an upper bound for $T$ since the density theorem tells us we can find $r\in Q\cap [a,b]$ such that $b^{\prime }<r<b$.