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Math Help - Writing domains

  1. #1
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    Writing domains

    I got a few problems regarding writing domains.

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

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

    3. For x=1 or 3<x<5, can I write \{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 f(x)=\frac{x+1}{x-1}, x\neq1.
    Instead of writing x\neq1, can I write x \in \mathbb{R}\backslash \{1\}

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

    3. For x=1 or 3<x<5, can I write \{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 x \in \mathbb{R}\backslash \{1\} is more rigorous than "for x \neq 1", it makes it harder to read, and not everyone uses that notation for set difference, either.
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