9
$\begingroup$

I just came across this "subset" symbol in a PDF:

$\Omega \subsetneq T$

I've never seen it before, and I tried looking for it via Detexify (to no avail). What does it mean?

  • 6
    [subs$e$t definitions](http://en.wikipedia.org/wiki/Subset#Definitions)2012-01-17

2 Answers 2

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This means $\Omega$ is a proper subset of $T$. That is, $\Omega\subseteq T$ but $\Omega \neq T$.

For example, $\{1, 2, 3\}\subsetneq \{1, 2, 3, 4\}$.

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    Well, people *sometimes* just use $\subset$ to mean $\subseteq$. Because it is quicker to type, perhaps? Context is all-important!2012-01-17
12

$\subsetneq$ ($\text{"\\subsetneq"}$) means: subset, but not equal.

Here's a nice example:

Let Ω be a half-strip in the complex plane: $ \Omega = \{ z \in \mathbb{C} | x_1 \leq \mathrm{Re} (z) \leq x_2 \text{ and } \mathrm{Im} (z) \geq y_0 \} \subsetneq \mathbb{C}. \, $