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Assume that $L$ is a language, is there any established notation that means that $L$ is infinite or empty?

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    $\begingroup$ For a language $L$, we generally say that $L=\varnothing$ or $L=\emptyset$ to mean $L$ is empty. There's no simple term I know of to indicate that $L$ is infinite, though you'll often see the informal expression $|\,L\,|=\infty$. $\endgroup$ – Rick Decker Dec 11 '15 at 16:46
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The usual way to describe these properties is by indicating the size of $L$, denoted by $|L|$.

  • Empty language, the size is zero, $|L|=0$
  • Finite language, $|L|=c$ or in general, the size in non-infinite, $|L|< \infty$
  • Infinite language, $|L|=\infty$.
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  • $\begingroup$ To summarize, the statement in the question can be written as $|L| \in \{0, \infty\}$ or $|L| \not\in \mathbb{N}$ (assuming $0 \not\in \mathbb{N}$). Nitpick note: we usually say cardinality instead of "size" when sets are concerned. $\endgroup$ – Raphael Dec 11 '15 at 17:19

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