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Thread: Writing domains

  1. #1
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    Writing domains

    I got a few problems regarding writing domains.

    1. If $\displaystyle f(x)=\frac{x+1}{x-1}$, $\displaystyle x\neq1$.
    Instead of writing $\displaystyle x\neq1$, can I write $\displaystyle x \in \mathbb{R}\backslash \{1\}$

    2. For the range $\displaystyle x<-1$ or $\displaystyle x>1$, can I write $\displaystyle \mathbb{R} \backslash [-1,1]$

    3. For $\displaystyle x=1$ or $\displaystyle 3<x<5$, can I write $\displaystyle \{1\} \cup (3,5)$. Can I treat intervals as a set and union with other sets?

    Thanks a lot for those who help!
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  2. #2
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    Quote Originally Posted by acc100jt View Post
    I got a few problems regarding writing domains.

    1. If $\displaystyle f(x)=\frac{x+1}{x-1}$, $\displaystyle x\neq1$.
    Instead of writing $\displaystyle x\neq1$, can I write $\displaystyle x \in \mathbb{R}\backslash \{1\}$

    2. For the range $\displaystyle x<-1$ or $\displaystyle x>1$, can I write $\displaystyle \mathbb{R} \backslash [-1,1]$

    3. For $\displaystyle x=1$ or $\displaystyle 3<x<5$, can I write $\displaystyle \{1\} \cup (3,5)$. Can I treat intervals as a set and union with other sets?
    1. Yes.
    2. Yes.
    3. Yes.
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  3. #3
    Member rowe's Avatar
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    I would suggest you always go for the simplest, easiest to read notation. While $\displaystyle x \in \mathbb{R}\backslash \{1\}$ is more rigorous than "for $\displaystyle x \neq 1$", it makes it harder to read, and not everyone uses that notation for set difference, either.
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