And there's this whole thing called Type 1 Zeno

and Type 2 Zeno, which is studied in the lectures.

We're going to deal with Type 1 Zenoes, because we know how to deal with them.

Type 2 Zenoes are tough, and we're not going to

deal with them here, in this class at least.

And an example is that, okay, you're given a system,

right?

This is a simple system here of two states, and you want

to see if this guy here is Type 1 Zeno or not.

And once again, just remember that this effect happens when

you have, lets say, the same guard condition, but just flipped, right?

So this was g1 and g2, it's possible that you did not keep going between the

states really fast.

But because it's the same condition here, g of x, which is less than 0, and then

greater or equal to 0, that's the only way you get this surface g of x

equal to 0, along which you're going to keep moving like this, right?

Okay.

So when is it going to be Type 1 Zeno?

This is the first question you ask when you're designing a system here.

And you have certain conditions for it.

These are the conditions.

Basically, what you want to see is that this is my surface g of x equal to 0.

And when I'm hitting the surface from whichever direction I'm coming, either

I'm coming from greater than equal to 0 or less than 0, right?

Whichever condition I'm coming from, when I hit the

surface does this particular equation hold true or not?

Or does this particular condition

hold true or not?

Which is simply just saying that whenever I hit

a surface, is it true that one mode, or

f1 for example, is pulling me in one direction,

and f2 is pulling me in the other direction?

And that's encoded in this condition here.

So it's not always true.

So that's why you want to check when is it going to be

true that I'm being pulled into different directions when I hit

the surface, which is g of x equal to 0. Okay, so this is pretty simple.