What does this answer mean? (continuous functions)

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SUMMARY

The discussion centers on the interpretation of the interval of existence for the function f(x) = [-x1/|X|^3, -x2/|X|^3]. The notation "E = R2 ~ {0}" indicates that the function is defined for all points in R² except the origin (0,0), which is excluded due to the denominator |X|^3 being undefined at that point. The correct mathematical representation of this exclusion is R² \ { (0,0) }. The participants clarify that the function remains continuous for all other values in R².

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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.
 
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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.
 

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