Fundamental Groups of the Mobius Band

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Seems to be isomorphic to Z, but I can't seem to be able to prove it.

Am I right? If I am, how do I prove it?
 
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Sounds good. Just by shrinking?

Maybe it's easier that I thought.
 
Or you could write down the universal cover and work out the group of deck transformations. Which is just as easy.
 
You lost me there - don't know what a "universal cover" is.
 

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