[AndrewC]

Were you wrong to claim that rational arithmetic is closed under all the operations in that equation?

And I'll make it easy for you. No, not in the context for which I made the statement. The infinite symbol was given special attention for a reason. It was to set up the next statement. The one which troubles you so much.

[edsheppa]

So you actually think that rational arithmetic is closed under all the operations in that equation? Really?