# Complete Partial Orders

• March 10th 2010, 06:19 AM
sm87
Complete Partial Orders
Can anybody show me how to solve this:
∑∞ is a complete partial order
thanks!

(sigma to the power of infinity is a complete partial order)
• March 10th 2010, 06:30 AM
Drexel28
Quote:

Originally Posted by sm87
Can anybody show me how to solve this:
∑∞ is a complete partial order
thanks!

(sigma to the power of infinity is a complete partial order)

What is $\Sigma^{\infty}$?
• March 10th 2010, 06:35 AM
sm87
Its a set of all finite and infinite strings over an alphabet ∑.
The main focus of the question is on the completeness of this poset i.e. showing
that each directed set in ∑∞ has a supremum.