Question 80
A set $M$ of real numbers will be called *special* if it has the properties:
(i) for each $x, y \in M$, $x \neq y$, the numbers $x+y$ and $xy$ are not zero and exactly one of them is rational;
(ii) for each $x \in M$, $x^2$ is irrational.
Find the maximum number of elements of a special set.
(i) for each $x, y \in M$, $x \neq y$, the numbers $x+y$ and $xy$ are not zero and exactly one of them is rational;
(ii) for each $x \in M$, $x^2$ is irrational.
Find the maximum number of elements of a special set.