What I am asking is, regarding the notation I used above for f(x)>0, could you please confirm that is correct? IS this set or itnerval notation?
I was doing some questions and the answers said that set notation was required, but I can't see why we cannot use interval notation(like I believe I have). Could you please provide an example of the 'correct' notation that you would use please?
And why have the answers said that I am wrong in using interval notation? Why is using my notation wrong for this question is the main issue that I have.
Sorry for the confusion. If my question does not make sense, please let me know so I can clarify.
Thanks for your help!
The notation \(\{x:f(x)>0\}\) is perfectly fine and reads: "the set of all values \(x\) such that \(f(x)\) is greater than \(0\)".
The notation you provided, \(\{x:x>2\}\cup \{x:x<-1\}\), is not 'interval notation'. The corresponding 'interval notation' would be \((-\infty,\,-1)\cup(2,\,\infty)\).
If a question specifies a required form for your answer, you must adhere to the instructions and do so. Otherwise, use any notation you want. For example, all the following are equivalent:\[(-2,\,-1)\cup [0,\,\infty)\qquad \{x\in\mathbb{R}\mid -2<x<-1\}\cup \{x\in\mathbb{R}\mid x\geq 0\}\qquad \mathbb{R}^+\cup (-2,\, -1)\cup\{0\}\] For this particular set of numbers, I prefer the first one because I believe it's the easiest to understand, but feel free to use whatever you want if the question allows you to.