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Math Help - Question on intervals

  1. #1
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    Question on intervals

    My question is:

    i) Is the following statement true or false, and explain why: "If a is less than or equal to b, then (-infinity, a) is a subset of (-infinity, b)".

    I drew a diagram which showed that this was true, but how would you go about proving it formally?

    Any help would be appreciated
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  2. #2
    Senior Member jakncoke's Avatar
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    Re: Question on intervals

    Assume  a \leq b then if a number  p \in (-\infty, a) then  p < a , so  p < a \leq b thus  p < b so  p \in (-\infty, b)
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  3. #3
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    Re: Question on intervals

    The standard way to prove "A is a subset of B" is to start "if x\in A, then use the definitions of A and B to conclude " x\in B".

    To prove "If a is less than or equal to b, then (-infinity, a) is a subset of (-infinity, b)":
    If p\in (-\infty, a) then p< a. Since a\le b and "<" is transitive, p<a\le b so p\in (-\infty, b).
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