Prove by contradiction that the interval 3 4 has no minimum

Prove by contradiction that the interval (3, 4) has no minimum element.

Solution

assume it had a minimum element .

that means that if we plot a point on the number line , we cannot a point lesser than the point . which is obviously not true

since for every x belonging to any interval a to b , we can find a value x - delta where delta tnds to zero and hence a lesser value than x

hence proved.