# Converting to predicate logic

I having a lot of trouble converting two english statements to predicate logic:

1. For every positive real number x, there is some real number y that is the square root of x (extend this statement to show that there are two distinct square roots of x)

2. For any two distinct real numbers there is a third real number with a value between the first two.

I figured out the first part of the first statement : ∀x (x > 0 → ∃y (y=$$\sqrt{x}$$)) but I am unable to solve the second part (extend this statement to show that there are two distinct square roots of x)

and I am clueless how to go about the second question (For any two distinct real numbers...)

Any help will be greatly appreciated!!

You can reformulate the parenthesized sentence into: For any positive real $$x$$ there exist numbers $$y_1$$ and $$y_2$$ such that they are not equal and such that each of them is a square root of $$x$$. I would write "$$y$$ being a square root of $$x$$" as $$y^2=x$$, since $$\sqrt{x}$$ is not unique in your statement.
For the second part: For any two $$x_1$$ and $$x_2$$ which are not equal there exists $$y$$ such that ($$x_1$$ is smaller than $$y$$ and $$y$$ is smaller than $$x_2$$) or ($$x_2$$ is smaller than $$y$$ and $$y$$ is smaller than $$x_1$$).