Definition of g.l.b and l.u.b:
In mathematics, g.l.b (greatest lower bound) and l.u.b (least upper bound) are concepts used in the theory of sets, particularly in the context of ordered sets. The g.l.b is the greatest element of a set that is less than or equal to all other elements in the set, while the l.u.b is the smallest element that is greater than or equal to all other elements in the set.

Understanding the expression x^2, x^2, 9:
The expression x^2, x^2, 9 represents a set of three elements. The first two elements are x^2, which means "x squared", and the third element is the constant 9.

Identifying the g.l.b:
To find the g.l.b of the set, we need to determine the greatest element that is less than or equal to all other elements in the set.

Element 1: x^2
Since x^2 can take any real value, there is no specific greatest lower bound for this element.

Element 2: x^2
Similarly, x^2 can also take any real value, so there is no specific greatest lower bound for this element.

Element 3: 9
The greatest lower bound for the constant 9 is 9 itself, as there is no element in the set that is less than 9.

Conclusion:
Since there is no specific greatest lower bound for the elements x^2 and x^2, the g.l.b of the set x^2, x^2, 9 does not exist.

Identifying the l.u.b:
To find the l.u.b of the set, we need to determine the smallest element that is greater than or equal to all other elements in the set.

Element 1: x^2
Similar to the g.l.b analysis, x^2 can take any real value, so there is no specific least upper bound for this element.

Element 2: x^2
Again, x^2 can also take any real value, so there is no specific least upper bound for this element.

Element 3: 9
The least upper bound for the constant 9 is 9 itself, as there is no element in the set greater than 9.

Conclusion:
Since there is no specific least upper bound for the elements x^2 and x^2, the l.u.b of the set x^2, x^2, 9 does not exist.

Summary:
The g.l.b and l.u.b of the set x^2, x^2, 9 do not exist because the elements x^2 and x^2 can take any real value, and there is no specific lower or upper bound. The only element with a specific lower and upper bound is the constant 9, which is its own g.l.b and l.u.b.