Actual Infinity in Reality?

[GrandizerII]

Steve,

Sorry to be late in the conversation.  But I really am puzzled as to why you think ifinities pose a logical contradiction as opposed to being hard to show in reality. 

I think the hotel idea sounds intuitively wrong to you merely because it's mathematical.   Infinite odd and infinite even numbers may feel wrong but isn't.  Think of it without numbers.  Suppose there is an infinite number of smoking rooms and an infinite number of non smoking rooms.  Two infinities of different kinds of things.  Together, both are infinite, yet you have twice as many room choices should you  be ambivalent to smoke.  

If that's still too close, consider infinite cats and infinite dogs .  Both infinities together are infinite pets.  Still infinity but with more choices.  

No logical contradiction.  Just more kinds in the omega.

Yep both are without ends so naturally the total set will be without end as well.