What does this answer mean? (continuous functions)

[spaderdabomb]

Working on some problems that have vectors, for example

f(x) = [-x₁/|X|³, -x₂/|X|³]

And then I am asked to find the largest interval of existence. The answer says "E = R² ~ {0}.

I'm not sure what this means. Does it mean the interval of existence is everywhere except 0? Is that what the ~ {0} means? It seems like the answer is that any x1, x2 value in R2 space satisfies continuity, but then I have no idea where the ~{0} comes from.

 

[jbunniii]

Yes, given the context I'm sure it means "every point in $\mathbb{R}^2$ except the origin. A more standard notation would be $\mathbb{R}^2 \setminus \{(0,0)\}$. By the way, this set isn't an interval at all.

The reason $(0,0)$ is excluded is because your function is not even defined there because of the $|x|^3$ in the denominator.