1: The title is indeed the correct way to react to learning this fact. 2: I’d like to explicitly point out that for linear functions, all you need to check is continuity at 0, which in other words means you only need to check that it’s bounded, where ‘bounded’ here means that if I send in a vector of size 1, I don’t get something of unbounded size.
That is, for linear functions, the only way a discontinuity can happen is if the unit sphere “blows up” when you send it into the function.
1: The title is indeed the correct way to react to learning this fact.
2: I’d like to explicitly point out that for linear functions, all you need to check is continuity at 0, which in other words means you only need to check that it’s bounded, where ‘bounded’ here means that if I send in a vector of size 1, I don’t get something of unbounded size.
That is, for linear functions, the only way a discontinuity can happen is if the unit sphere “blows up” when you send it into the function.