Consider the set of real numbers under the operation of addition.

a) Is the system closed? Explain.

b) Is there an identity element? If so, what is it?

c) Does each element in the set have an inverse? Explain.

d) The associative property holds. Provide one example to demonstrate the associative property.

e) The commutative property holds. Provide one example to demonstrate the commutative property.

f) Is this mathematical system a commutative group? Explain.