# Why is $\mu$ finite looping?

It is said that the intuitive meaning of $\mu$ is finite looping where as the intuitive meaning of $\nu$ is infinite looping in $\mu$ calculus. I understand this for finite systems, but why is this true in general?

Is there any theorem which proves this ?

• Who says so? In particular, $\nu$ is new to me.
– Raphael
Nov 26, 2017 at 21:04
• What context is this in? $\mu$ and $\nu$ are commonly used for least-fixed point and greatest-fixed point in PL-theory, is this what you mean? Mar 27, 2018 at 1:03

• 1) No Turing-complete model has an uncountable number of states. 2) (Bounded) $\mu$ has known bounds, by definition. (Unbounded $\mu$ aka) $\nu$ has not. That is, if you're using the definitions I know. You don't say which you're using.