"such that" logical symbol So, in the definition of what is a square root,


  $\sqrt{x}$ are all numbers $y$ such that $y×y=x$.


are there any logical mathematical symbols so that the above definition can be written using logical operators only, and no natural language?

Where can I get some introductory or reference material on all such logical symbols?

update:
I noticed, some time after asking the question that the definition of square root I am giving is wrong. The square root of $x$ is to defined to be the non-negative number $y$ that satisfies $y*y=x$. But the question was about notation, not square roots, so I am leaving it as it stands due to some answers using the supplied (erroneous) definition.
You could write this in a few different ways... I'm not sure what you're asking, so let me show you a couple.

For one, you could define the condition $y\in\text{Sqrt}(x)$, rather than the set itself:
$$
y\in\text{Sqrt}(x)\Leftrightarrow y^2=x
$$

The following two are commonly used in set definitions:
$$
\text{Sqrt}(x)=\{y\mid y^2=x\}\qquad \text{or}\qquad \text{Sqrt}(x)=\{y:\ y^2=x\}
$$

I also see people use (and have used myself) "s.t." as an abbreviation for such that in formulas.
I ALSO have seen a backwards ∈ symbol for "such that."  I saw it in logical notation for the definition of the limit of a function. M. Del Nero