Real numbers and rational number I know I am getting somewhere wrong but my question is how rational numbers are real numbers(Q is subset of R) .Rational numbers don't have least upperbound property and lub property is necessary condition for being real numbers
A bounded subset of the rational numbers has a least upper bound in the real numbers, but not necessarily in the rational numbers.

Many subsets of the real numbers do not have the least upper bound property (within themselves).  For instance, the irrational numbers do not have the least upper bound property.  That is, there are bounded sets of irrational numbers that do not have a least upper bound in the irrationals.  Of course they still have a least upper bound in the reals (but that least upper bound would be rational).
Every rational real is the lub of itself.