# There is any notation for a language that is empty infinite?

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

• 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 $|\,L\,|=\infty$. – Rick Decker Dec 11 '15 at 16:46

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, $|L|=\infty$.
• 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. – Raphael Dec 11 '15 at 17:19