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I'm reading a textbook on complex analysis and I've come across notation using this ($\in$) symbol. In the context of "an argument of $z = x + iy$ is a number $\phi \in \mathbb R$ such that $x = r\cos\phi$ and $y = r\sin\phi$" what does this symbol mean?

Mauro ALLEGRANZA
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LoreleiRS
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    "Element of". It's universal, has nothing to do with complex analysis, $x\in S$ means $x$ is an element of the set (or class) $S$. – Daniel Fischer Apr 16 '14 at 13:40
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    Mandatory Wikipedia link. – fuglede Apr 16 '14 at 13:44
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    And $R$ here is the set of real numbers. So “a number $\varphi\in R$” is an obscure way to write “a real number $\varphi$”. – MJD Apr 16 '14 at 13:47
  • "obscure way"... :-P – Ant Apr 16 '14 at 13:51
  • $\in$ is atomic and has no definiton – Amr Apr 16 '14 at 13:58
  • @Amr: Some people might beg to differ. – Asaf Karagila Apr 16 '14 at 15:35
  • @AsafKaragila Since you know a looot more than I do in set theory, I 'd like to hear your view about what I said – Amr Apr 16 '14 at 15:52
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    @Amr: The prime relation in New Foundations is in fact $\subseteq$, and you define $x\in y\iff {x}\subseteq y$. In algebraic theories the $\in$ relation is in fact defined by arrows, which are closer to functions than to the $\in$ membership, that is $\pi\in\Bbb R$ is translated to the statement that there is an arrow from a singleton into $\Bbb R$ and $\pi$ is its range (or image). In both these contexts, $\in$ is not the atomic relation; although personally, I am philosophically inclined to agree with your original comment. – Asaf Karagila Apr 16 '14 at 15:58
  • Curious, which complex analysis textbook are you reading? – bonsoon Apr 27 '14 at 10:01

3 Answers3

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$\phi\in R$ just means that $\phi$ is an element of $R$.

In this case it would mean that $\phi$ is an element of the set of real numbers, $\mathbb{R}$.

amWhy
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Euna
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As $\in$ has $\LaTeX$ code of \in, $\phi\in\mathbb{R}$ means $\phi$ is element of set of real number $\mathbb{R}$.

aaa
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$\in$ means "is an element of", or "is in". If I had a set $S = \{1,2,3\}$, then $1 \in S$, but $4 \notin S$.

Future
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  • When posting an answer to a two-years old question, it is expected that you add information not present in the other two answers that were posted in a timely manner. – Asaf Karagila Jan 22 '16 at 08:57