[neutralino]

Originally Posted by AntonioLao Now that I thought about it some more the cardinality of the Moebius strip is really infinity.

Cardinality is normally, at least colloquially, described as a measure of the number of elements in a given set. I'm not quite sure what you mean by the cardinality of a surface: are you talking about the number of points on the surface? Also, a cardinality of infinity doesn't really mean much: as you mention above, the number of elements in |R is greater than the number of elements in |N, but they are both infinite sets. What do you mean by a cardinality of infinity here?