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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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  • $\begingroup$ That's the same thing. The set of real numbers is the whole interval $(-\infty,+\infty)$. $\endgroup$
    – Julien
    May 10, 2013 at 0:05
  • $\begingroup$ @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... :) $\endgroup$
    – apnorton
    May 10, 2013 at 0:09
  • $\begingroup$ @anorton Hmm...you might very well be right. $\endgroup$
    – Julien
    May 10, 2013 at 0:11

1 Answer 1

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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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