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$\{3\}$ is a subset of $(0, 3)$, true or false?

I'm inclined to say true, however my textbook is indicating that it's false because $\{3\}$ is a set and $(0,3)$ is an interval. Perhaps I'm reading that out of context. Am I on the right path?

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Is $3 \in (0, 3) = \{x \text{ a real number} \mid 0 < x < 3\}$? –  Dylan Moreland Sep 3 '12 at 1:09
    
Remember $a\in A \iff \{a\} \subset A$ –  Pedro Tamaroff Sep 3 '12 at 1:11
    
Also, what Dylan said. –  Pedro Tamaroff Sep 3 '12 at 1:11
    
The notation $(0,3)$ is a set and denotes the set $\lbrace x \vert 0 < x < 3 \rbrace$, that is all real numbers between 0 and 3, not including 0 and 3. –  Kris Williams Sep 3 '12 at 1:11
    
awesome, thanks for the insight. This text is as clear as mud sometimes! –  electr0hed Sep 3 '12 at 1:13

1 Answer 1

up vote 1 down vote accepted

No $3\not\in (0,3)$. Threfore, $\{3\}$ cannot be a subset of $(0,3)$.

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Awesome, thanks for the insight. This text is as clear as mud sometimes! –  electr0hed Sep 3 '12 at 1:17

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