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when we say that a solution is true for $-\infty < x < +\infty$ does that mean that it is true for all real numbers or any number between negative infinity and positive infinity, which is quite vague.

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That's the same thing. The set of real numbers is the whole interval $(-\infty,+\infty)$. –  1015 May 10 '13 at 0:05
    
@julien I think that his/her second interpretation is intended to say "a particular $x$ value in range $(-\infty, +\infty)$". At least, that's how I read it... :) –  anorton May 10 '13 at 0:09
    
@anorton Hmm...you might very well be right. –  1015 May 10 '13 at 0:11
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up vote 2 down vote accepted

When we say solutions exist for $-\infty \lt x \lt +\infty$, we are saying the solution is valid for all $x$ in that range. So, your first statement is the correct interpretation.

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