Hello guys,

since there is no section "Topology" or "Logic", I think "Advanced Algebra" is yet the closest.

I've come upon the term "filter" in Mathematics. Principally, I have no problem understanding it - however there is one point in the

definition that I don't understand. It is as follows:

Be $\displaystyle (P, \leq)$ a partially ordered set and F a subset. Then F is a filter iff

1. ...

2. $\displaystyle \forall x,y \in F \ \exists \ z \in F : z \leq x \ \text{and} \ z \leq y $

3. ...

Now the question arises with 2.: Why do I needtwoelements x,y to be greater or equal to z? Why is one not enough, and why do I not need three or something? What exactly does that mean?

Thanks in advance.