# Thread: Notation (Underbar and Overbar)

1. ## Notation (Underbar and Overbar)

$\epsilon_t$ is generated from the stationary Markov distribution function $\Phi (\epsilon_t | \epsilon_{t-1})$ defined on the domain $Q=[\underline{\epsilon}, \bar \epsilon]$

What does that last term mean? Specifically, what's the epsilon underbar and epsilon overbar stuff?

2. I believe that means infimum and supremum.

So the interval is the "stretchy" min and max of $\epsilon.$

3. Originally Posted by Anonymous1
I believe that means infimum and supremum.

So the interval is the "stretchy" min and max of $\epsilon.$
Can you expand on what that means in this context?

4. Engineering proof: by example.

Say we have a set $A: a\in [0,1).$ What is the maximum? The answer is, there is no maximum. This is because there are infinitely many numbers between any two points. So, we call $1$ the $supremum$ of the set $A.$

Like a banished emperor, it rules from without.

5. Originally Posted by Anonymous1
Engineering proof: by example.

Say we have a set $A: a\in [0,1).$ What is the maximum? The answer is, there is no maximum. This is because there are infinitely many numbers between any two points. So, we call $1$ the $supremum$ of the set $A.$

Like a banished emperor, it rules from without.
Wow, great imagery re: the emperor!

I can see why there is no max in $[0,1)$, but that's because the right hand side is open. If the closed set $
Q=[\underline{\epsilon}, \bar \epsilon]
$
is to have no max or min, it must be because of some meaning of the underbarred/overbarred epsilons, no?

6. The set INCLUDES the infimum and supremum. This may not be of great concern to you anyhow, and it may just mean min and max. Post back if any issues arise.