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Math Help - Combining chained inequalities

  1. #1
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    Combining chained inequalities

    I've written a proof which ends with the (simplified) statement:

    "Statement A is true iff a<x<b OR b<x<a"

    This is because b is not necessarily greater than a. In plain English, "Statement A is true if and only if x is between values a and b"

    I wonder if there is some way of combining the chained inequalities, hence being able to get rid of OR.

    Many thanks
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  2. #2
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    You could say, min(a,b) < x < max(a,b) or maybe x = at + b(1 - t) for some 0 < t < 1 if a and b are real numbers. Probably the simplest way is what you said, x is between a and b.
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  3. #3
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    Quote Originally Posted by sevenquid View Post
    I've written a proof which ends with the (simplified) statement: "Statement A is true iff a<x<b OR b<x<a"
    I have just returned from a St. Patrick’s Day party (late of course). Why do Anglicans have such parties? I guess an Irish family name makes it OK.
    Anyway, having time on my hands having been dragged there by my wife, I thought about this question. Again, it just popped into the ole brain with the help of Guinness.
    Do it with a distance function. c is between a~\&~b if and only if a,~b,~\&~c are three numbers such that |a-b|=|a-c|+|c-b|.
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