Fields

Check that the real numbers form a field.

Prove that these are fields.

• (a)  The rational numbers $\mathbb{Q}$     (b)  The complex numbers $\mathbb{C}$

Give an example that shows that the integer number system is not a field.

Check that the set $\mathbb{B}=\text{$\{\hskip 1.00006pt0,1\hskip 1.00006pt\}$}$ is a field under the operations listed above,

Give suitable operations to make the set $\{\hskip 1.00006pt0,1,2\hskip 1.00006pt\}$ a field.