Algebra: What does "is defined for" mean? In algebra what does: "Is defined for" mean?

I have a question posted:


  $\sqrt{a+b}$ is defined for $-b \leq a$.


The question posed is: Is this true...

My question: WHAT DOES "Is Defined For" mean??
During philosophy class, and independent of that specific class, a math professor simply claimed that "is defined for" is best understood as an axiom and a bridge for us to understand conditions. We can't really use logic to define it, since we defined logic through the use of "is defined for". 

Another way of putting it is to go the other way around; we can express the proposition "is defined for" through the use of logical symbols, and we define "is defined for" through those. 

In this context, you could probably translate it to "is only true for the condition of". 

Edit: it appears I missunderstood the question - yes, I'm trying to present the idea of how to define defined
It means, that the square root function $\sqrt{a+b}$ is properly defined, when you satisfy the given condition, in your example:
$$-b\leq a$$
E.g. for $b = 3$ and $a = -5$, then the inequality is not satisfied, because
$$
-b = -3 \nleq -5 = a.
$$
When we work in $\mathbb{R}$ then square root $f(x)=\sqrt{x}$is not defined for $x &lt; 0$. So with  $b = 3$ and $a = -5$ the expression would be $\sqrt{a + b} =\sqrt{-5 + 3} = \sqrt{-2} $.